Brendle, Simon 1981
Overview
Works:  17 works in 35 publications in 3 languages and 414 library holdings 

Roles:  Author, Contributor, Thesis advisor, Author of introduction 
Publication Timeline
.
Most widely held works by
Simon Brendle
Ricci flow and the sphere theorem by
Simon Brendle(
Book
)
10 editions published in 2010 in English and held by 214 WorldCat member libraries worldwide
"In 1982, R. Hamilton introduced a nonlinear evolution equation for Riemannian metrics with the aim of finding canonical metrics on manifolds. This evolution equation is known as the Ricci flow, and it has since been used widely and with great success, most notably in Perelman's solution of the Poincare conjecture. Furthermore, various convergence theorems have been established. This book provides a concise introduction to the subject as well as a comprehensive account of the convergence theory for the Ricci flow. The proofs rely mostly on maximum principle arguments. Special emphasis is placed on preserved curvature conditions, such as positive isotropic curvature. One of the major consequences of this theory is the Differentiable Sphere Theorem: a compact Riemannian manifold, whose sectional curvatures all lie in the interval (1,4], is diffeomorphic to a spherical space form. This question has a long history, dating back to a seminal paper by H.E. Rauch in 1951, and it was resolved in 2007 by the author and Richard Schoen."Publisher's description
10 editions published in 2010 in English and held by 214 WorldCat member libraries worldwide
"In 1982, R. Hamilton introduced a nonlinear evolution equation for Riemannian metrics with the aim of finding canonical metrics on manifolds. This evolution equation is known as the Ricci flow, and it has since been used widely and with great success, most notably in Perelman's solution of the Poincare conjecture. Furthermore, various convergence theorems have been established. This book provides a concise introduction to the subject as well as a comprehensive account of the convergence theory for the Ricci flow. The proofs rely mostly on maximum principle arguments. Special emphasis is placed on preserved curvature conditions, such as positive isotropic curvature. One of the major consequences of this theory is the Differentiable Sphere Theorem: a compact Riemannian manifold, whose sectional curvatures all lie in the interval (1,4], is diffeomorphic to a spherical space form. This question has a long history, dating back to a seminal paper by H.E. Rauch in 1951, and it was resolved in 2007 by the author and Richard Schoen."Publisher's description
Ricci flow and the sphere theorem by
Simon Brendle(
)
3 editions published in 2010 in English and held by 65 WorldCat member libraries worldwide
"In 1982, R. Hamilton introduced a nonlinear evolution equation for Riemannian metrics with the aim of finding canonical metrics on manifolds. This evolution equation is known as the Ricci flow, and it has since been used widely and with great success, most notably in Perelman's solution of the Poincare conjecture. Furthermore, various convergence theorems have been established. This book provides a concise introduction to the subject as well as a comprehensive account of the convergence theory for the Ricci flow. The proofs rely mostly on maximum principle arguments. Special emphasis is placed on preserved curvature conditions, such as positive isotropic curvature. One of the major consequences of this theory is the Differentiable Sphere Theorem: a compact Riemannian manifold, whose sectional curvatures all lie in the interval (1,4], is diffeomorphic to a spherical space form. This question has a long history, dating back to a seminal paper by H.E. Rauch in 1951, and it was resolved in 2007 by the author and Richard Schoen."Publisher's description
3 editions published in 2010 in English and held by 65 WorldCat member libraries worldwide
"In 1982, R. Hamilton introduced a nonlinear evolution equation for Riemannian metrics with the aim of finding canonical metrics on manifolds. This evolution equation is known as the Ricci flow, and it has since been used widely and with great success, most notably in Perelman's solution of the Poincare conjecture. Furthermore, various convergence theorems have been established. This book provides a concise introduction to the subject as well as a comprehensive account of the convergence theory for the Ricci flow. The proofs rely mostly on maximum principle arguments. Special emphasis is placed on preserved curvature conditions, such as positive isotropic curvature. One of the major consequences of this theory is the Differentiable Sphere Theorem: a compact Riemannian manifold, whose sectional curvatures all lie in the interval (1,4], is diffeomorphic to a spherical space form. This question has a long history, dating back to a seminal paper by H.E. Rauch in 1951, and it was resolved in 2007 by the author and Richard Schoen."Publisher's description
Geometry and topology : lectures given at the Geometry and Topology conferences at Harvard University in 2011 and at Lehigh
University in 2012(
Book
)
1 edition published in 2013 in English and held by 59 WorldCat member libraries worldwide
This volume includes papers presented by several speakers at the Geometry and Topology conferences at Harvard University in 2011 and at Lehigh University in 2012. Included are works by Simon Brendle, on the Lagrangian minimal surface equation and related problems; by Sergio Cecotti and Cumrun Vafa, concerning classification of complete N=2 supersymmetric theories in four dimensions; by F. Reese Harvey and H. Blaine Lawson Jr., on existence, uniqueness, and removable singularities for nonlinear PDEs in geometry; by János Kollár, concerning links of complex analytic singularities; by Claude LeBrun, on Calabi energies of extremal toric surfaces; by MuTao Wang, concerning mean curvature flows and isotopy problems; and by Steve Zelditch, on eigenfunctions and nodal sets
1 edition published in 2013 in English and held by 59 WorldCat member libraries worldwide
This volume includes papers presented by several speakers at the Geometry and Topology conferences at Harvard University in 2011 and at Lehigh University in 2012. Included are works by Simon Brendle, on the Lagrangian minimal surface equation and related problems; by Sergio Cecotti and Cumrun Vafa, concerning classification of complete N=2 supersymmetric theories in four dimensions; by F. Reese Harvey and H. Blaine Lawson Jr., on existence, uniqueness, and removable singularities for nonlinear PDEs in geometry; by János Kollár, concerning links of complex analytic singularities; by Claude LeBrun, on Calabi energies of extremal toric surfaces; by MuTao Wang, concerning mean curvature flows and isotopy problems; and by Steve Zelditch, on eigenfunctions and nodal sets
Oneparameter semigroups for linear evolution equations by
KlausJochen Engel(
Book
)
5 editions published between 2000 and 2008 in English and Italian and held by 41 WorldCat member libraries worldwide
"This book gives an uptodate account of the theory of strongly continuous oneparameter semigroups of linear operators. It includes a systematic discussion of the spectral theory and the longterm behavior of such semigroups. A special feature of the text is an unusually wide range of applications, to ordinary and partial differential operators, delay and Volterra equations and to control theory, et cetera, and an emphasis on philosophical motivation and the historical background."BOOK JACKET. "The book is written for students, but should also be of value for researchers interested in this field."Jacket
5 editions published between 2000 and 2008 in English and Italian and held by 41 WorldCat member libraries worldwide
"This book gives an uptodate account of the theory of strongly continuous oneparameter semigroups of linear operators. It includes a systematic discussion of the spectral theory and the longterm behavior of such semigroups. A special feature of the text is an unusually wide range of applications, to ordinary and partial differential operators, delay and Volterra equations and to control theory, et cetera, and an emphasis on philosophical motivation and the historical background."BOOK JACKET. "The book is written for students, but should also be of value for researchers interested in this field."Jacket
Krümmungsflüsse auf Mannigfaltigkeiten mit Rand by
Simon Brendle(
Book
)
3 editions published in 2001 in German and held by 12 WorldCat member libraries worldwide
3 editions published in 2001 in German and held by 12 WorldCat member libraries worldwide
Ramification theory for varieties over a local field(
Book
)
2 editions published in 2013 in English and held by 7 WorldCat member libraries worldwide
2 editions published in 2013 in English and held by 7 WorldCat member libraries worldwide
Oneparameter semigroups for linear evolution equations by
KlausJochen Engel(
Book
)
1 edition published in 1999 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 1999 in English and held by 6 WorldCat member libraries worldwide
The Ninth Takagi lectures 4 June 2011, Kyoto by
Carlos E Kenig(
Book
)
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
New results on the singularity analysis of the KaehlerRicci flow by Tsz Ho Fong(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
In this thesis, we study the singularity development of the KaehlerRicci flow on holomorphic fibrations, and classify the singularity models of some classes of fibrations using parabolic rescaling. We first study the collapsing behavior of CalabiYau fibrations under the KaehlerRicci flow. A compact Kaehler manifold with semiample canonical line bundle admits a fibration of CalabiYau manifolds with possibly singular fibers. The convergence behavior for this class of manifolds under the KaehlerRicci flow was first studied by Song and Tian who establish the metric convergence in the sense of currents. In this thesis, we obtain the optimal collapsing rate of the nonsingular CalabiYau fibers, thus improving Song and Tian's work in analytic and geometric aspects. Secondly, we focus on a specific type of holomorphic fibration, namely the CP^1bundles over KaehlerEinstein manifolds. Fiber collapsing in the sense of GromovHausdorff convergence was shown to occur in this case by Song, Szekelyhidi and Weinkove. We study the finitetime singularities for these manifolds using parabolic rescaling and dilation procedures adapted from Hamilton and Perelman in their works of the Ricci flow on 3manifolds. We prove that when the flow metric has cohomogeneity1 symmetry the collapsing occurs as a Type I singularity and we show that the singularity is modelled by C^n X CP^1
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
In this thesis, we study the singularity development of the KaehlerRicci flow on holomorphic fibrations, and classify the singularity models of some classes of fibrations using parabolic rescaling. We first study the collapsing behavior of CalabiYau fibrations under the KaehlerRicci flow. A compact Kaehler manifold with semiample canonical line bundle admits a fibration of CalabiYau manifolds with possibly singular fibers. The convergence behavior for this class of manifolds under the KaehlerRicci flow was first studied by Song and Tian who establish the metric convergence in the sense of currents. In this thesis, we obtain the optimal collapsing rate of the nonsingular CalabiYau fibers, thus improving Song and Tian's work in analytic and geometric aspects. Secondly, we focus on a specific type of holomorphic fibration, namely the CP^1bundles over KaehlerEinstein manifolds. Fiber collapsing in the sense of GromovHausdorff convergence was shown to occur in this case by Song, Szekelyhidi and Weinkove. We study the finitetime singularities for these manifolds using parabolic rescaling and dilation procedures adapted from Hamilton and Perelman in their works of the Ricci flow on 3manifolds. We prove that when the flow metric has cohomogeneity1 symmetry the collapsing occurs as a Type I singularity and we show that the singularity is modelled by C^n X CP^1
Elliptic and parabolic problems in conformal geometry by
Simon Brendle(
)
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
Wave equations on asymptotically de Sitter spaces by Dean Russell Baskin(
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
Asymptotically de Sitter spaces are Lorentzian manifolds modeled on the de Sitter space of general relativity. In this dissertation, we construct the forward fundamental solution for the wave and KleinGordon equations on asymptotically de Sitter spaces. We adapt classes of conormal and paired Lagrangian distributions to this setting and show that the lift of the kernel of the forward fundamental solution to a blownup space is a sum of distributions in these classes. We use the structure of the kernel of the fundamental solution to study its mapping properties. We show that Strichartz estimates with loss hold for the positive mass KleinGordon equation on asymptotically de Sitter spaces. When the mass parameter is the conformal value, Strichartz estimates hold without loss. As an application of these estimates, we prove a smalldata global existence result for a defocusing KleinGordon equation
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
Asymptotically de Sitter spaces are Lorentzian manifolds modeled on the de Sitter space of general relativity. In this dissertation, we construct the forward fundamental solution for the wave and KleinGordon equations on asymptotically de Sitter spaces. We adapt classes of conormal and paired Lagrangian distributions to this setting and show that the lift of the kernel of the forward fundamental solution to a blownup space is a sum of distributions in these classes. We use the structure of the kernel of the fundamental solution to study its mapping properties. We show that Strichartz estimates with loss hold for the positive mass KleinGordon equation on asymptotically de Sitter spaces. When the mass parameter is the conformal value, Strichartz estimates hold without loss. As an application of these estimates, we prove a smalldata global existence result for a defocusing KleinGordon equation
Decay of rhenish tuff in Dutch monuments(
)
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
On the freeboundary mean curvature flow by Nicholas Edelen(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
We investigate the freeboundary mean curvature flow. This is an evolution of surfaces by ``steepest descent for area, '' while preserving the Neumanntype condition that all the surfaces meet some fixed barrier orthogonally. For example, a bubble in a sink. We first prove the HuiskenSinestrari convexity estimates for freeboundary mean curvature flow, which classifies ``typeII'' singularities. We then develop the notion of weak freeboundary mean curvature flow, extending Brakke's original definition, and proving a local regularity theorem. We also prove a geometric eigenvalue gap estimate, extending results of AshbaughBenguria and BenguriaLinde
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
We investigate the freeboundary mean curvature flow. This is an evolution of surfaces by ``steepest descent for area, '' while preserving the Neumanntype condition that all the surfaces meet some fixed barrier orthogonally. For example, a bubble in a sink. We first prove the HuiskenSinestrari convexity estimates for freeboundary mean curvature flow, which classifies ``typeII'' singularities. We then develop the notion of weak freeboundary mean curvature flow, extending Brakke's original definition, and proving a local regularity theorem. We also prove a geometric eigenvalue gap estimate, extending results of AshbaughBenguria and BenguriaLinde
Regularity theory for the symmetric minimal surface equation by Kaveh Fouladgar(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
We consider the solutions of the symmetric minimal surface equation (SME), the geometric significance of which is that such solutions have symmetric graphs, which are minimal hypersurfaces. The SME has been previously studied by Dierkes, Huisken, and Simon. Using the uniform Holder continuity estimate for positive bounded solutions proved by Simon, we are able to define a singular solution of the SME as local uniform limits of sequences of positive solutions of the SME. Next, we study the existence of singular solutions, beginning with the observation that, by standard ODE theory, onedimensional singular solutions do not exist. However we will show, via a LeraySchauder argument, that in all dimensions greater than one there is rich class of singular solutions. Having established an existence theory for the SME, we focus on studying the regularity and singularity properties of singular solutions of the SME. More or less standard quasilinear elliptic theory shows that for any bounded positive solution of the SME there are local gradient bounds, and for positive solutions defined on the closure of a smooth convex domain there is a global gradient bound, depending only on the supremum and infimum of the solution and the domain. For singular solutions (or classes of positive solutions without a uniform positive lower bound), it will be shown that there is a local gradient estimate in a neighborhood of any singular point, depending only on the supremum of the solution and the distance of the singular point and the boundary of the domain. To establish these latter gradient estimates, we will use a modification of Simon's blow up of the Jacobi field argument together with the work of Ilmanen. As a consequence of gradient estimates, we are then able to show, via an application of the Federer dimension reducing argument, that the Hausdorff dimension of the singular set of an ndimensional SME is at most n2
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
We consider the solutions of the symmetric minimal surface equation (SME), the geometric significance of which is that such solutions have symmetric graphs, which are minimal hypersurfaces. The SME has been previously studied by Dierkes, Huisken, and Simon. Using the uniform Holder continuity estimate for positive bounded solutions proved by Simon, we are able to define a singular solution of the SME as local uniform limits of sequences of positive solutions of the SME. Next, we study the existence of singular solutions, beginning with the observation that, by standard ODE theory, onedimensional singular solutions do not exist. However we will show, via a LeraySchauder argument, that in all dimensions greater than one there is rich class of singular solutions. Having established an existence theory for the SME, we focus on studying the regularity and singularity properties of singular solutions of the SME. More or less standard quasilinear elliptic theory shows that for any bounded positive solution of the SME there are local gradient bounds, and for positive solutions defined on the closure of a smooth convex domain there is a global gradient bound, depending only on the supremum and infimum of the solution and the domain. For singular solutions (or classes of positive solutions without a uniform positive lower bound), it will be shown that there is a local gradient estimate in a neighborhood of any singular point, depending only on the supremum of the solution and the distance of the singular point and the boundary of the domain. To establish these latter gradient estimates, we will use a modification of Simon's blow up of the Jacobi field argument together with the work of Ilmanen. As a consequence of gradient estimates, we are then able to show, via an application of the Federer dimension reducing argument, that the Hausdorff dimension of the singular set of an ndimensional SME is at most n2
Microlocal analysis of lagrangian submanifolds of radial points by Nick Haber(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
Microlocal analysis relies on correspondences between quantum physics and classical physics to give information about certain PDEs  for instance, linear variablecoefficient PDEs on manifolds. PDEs are interpreted as quantum systems. The corresponding classical systems tell us, for example, function spaces on which problems are solvable or almost solvable, existence and uniqueness results, and the structure of solution operators. Landmark papers of Hörmander and Duistermaat and Hörmander establish key results for the standard calculus of microlocal analysis, which gives a broad framework for dealing with variablecoefficient PDEs on manifolds. Their work is wellsuited for dealing with PDEs which, in a generalized sense, are hyperbolic, with corresponding classical dynamics looking like wave propagation of geometric optics. In this thesis, we aim to extend many of their results to situations in which the corresponding classical dynamics are less wellbehaved: those with a Lagrangian submanifold of radial points
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
Microlocal analysis relies on correspondences between quantum physics and classical physics to give information about certain PDEs  for instance, linear variablecoefficient PDEs on manifolds. PDEs are interpreted as quantum systems. The corresponding classical systems tell us, for example, function spaces on which problems are solvable or almost solvable, existence and uniqueness results, and the structure of solution operators. Landmark papers of Hörmander and Duistermaat and Hörmander establish key results for the standard calculus of microlocal analysis, which gives a broad framework for dealing with variablecoefficient PDEs on manifolds. Their work is wellsuited for dealing with PDEs which, in a generalized sense, are hyperbolic, with corresponding classical dynamics looking like wave propagation of geometric optics. In this thesis, we aim to extend many of their results to situations in which the corresponding classical dynamics are less wellbehaved: those with a Lagrangian submanifold of radial points
On the variational methods for minimal submanifolds by Xin Zhou(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
In this thesis, we study two problems concerning variational methods for minimal submanifolds. Specifically we consider minmax theory for minimal surfaces. We construct the "saddle point" type critical points for the area functional, and study the geometrical properties of these. In the first part, we consider the mapping problem for the minmax theory. In particular, we prove an existence theorem for minmax minimal surfaces of arbitrary genus g ≥ 2 by variational methods. We show that the minmax critical value for the area functional can be achieved by the bubbling limit of branched minimal surfaces with nodes of genus g together with possibly finitely many branched minimal spheres. We also prove a strong convergence theorem similar to the classical mountain pass lemma. In the second part, we consider the geometric measure theory approach to the minmax theory. We study the shape of the minmax minimal hypersurface constructed by AlmgrenPitts corresponding to the fundamental class of a Riemannian manifold (M, g) of dimension n + 1 with positive Ricci curvature and 2 ≤ n ≤ 6. We characterize the Morse index, area and multiplicity of this minmax hypersurface. Precisely, we show that the minmax hypersurface is either orientable and of index one, or is a double cover of a nonorientable minimal hypersurface with least area among all closed embedded minimal hypersurfaces
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
In this thesis, we study two problems concerning variational methods for minimal submanifolds. Specifically we consider minmax theory for minimal surfaces. We construct the "saddle point" type critical points for the area functional, and study the geometrical properties of these. In the first part, we consider the mapping problem for the minmax theory. In particular, we prove an existence theorem for minmax minimal surfaces of arbitrary genus g ≥ 2 by variational methods. We show that the minmax critical value for the area functional can be achieved by the bubbling limit of branched minimal surfaces with nodes of genus g together with possibly finitely many branched minimal spheres. We also prove a strong convergence theorem similar to the classical mountain pass lemma. In the second part, we consider the geometric measure theory approach to the minmax theory. We study the shape of the minmax minimal hypersurface constructed by AlmgrenPitts corresponding to the fundamental class of a Riemannian manifold (M, g) of dimension n + 1 with positive Ricci curvature and 2 ≤ n ≤ 6. We characterize the Morse index, area and multiplicity of this minmax hypersurface. Precisely, we show that the minmax hypersurface is either orientable and of index one, or is a double cover of a nonorientable minimal hypersurface with least area among all closed embedded minimal hypersurfaces
The geometry of asymptotically hyperbolic manifolds by Otis Chodosh(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
We discuss the largescale geometry of asymptotically hyperbolic manifolds. Asymptotically hyperbolic manifolds arise naturally in general relativity. However, several fundamental questions about them remain unresolved, including the asymptotically hyperbolic Penrose inequality and the static uniqueness of the Schwarzschildantide Sitter metric. The main contributions of this thesis are twofold: Firstly, we introduce a new notion of renormalized volume for asymptotically hyperbolic manifolds and prove a sharp Penrosetype inequality where mass is replaced by renormalized volume. Secondly, we use the notion of renormalized volume to study isoperimetric regions in asymptotically hyperbolic manifolds. We prove that for initial data sets that are Schwarzschildantide Sitter at infinity and satisfy appropriate scalar curvature lower bounds, sufficiently large coordinate spheres are uniquely isoperimetric. This is relevant in the context of Bray's isoperimetric approach to the Penrose inequality. From a geometric viewpoint, our results show that the largescale geometry of asymptotically hyperbolic manifolds significantly differs from the more familiar asymptotically flat setting. The renormalized volume is a very different quantity from the ``mass, '' and our results suggest that it is a stronger quantity. As a consequence of this, we uncover a link between scalar curvature and the behavior of large isoperimetric regions, which is not present in the asymptotically flat setting. Additionally, we discuss isoperimetric regions in warped products and consequences for the renormalized volume of a more general class of metrics. Finally, we study rotational symmetry of expanding Ricci solitons, a problem that is formally similar to the static uniqueness question with negative cosmological constant
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
We discuss the largescale geometry of asymptotically hyperbolic manifolds. Asymptotically hyperbolic manifolds arise naturally in general relativity. However, several fundamental questions about them remain unresolved, including the asymptotically hyperbolic Penrose inequality and the static uniqueness of the Schwarzschildantide Sitter metric. The main contributions of this thesis are twofold: Firstly, we introduce a new notion of renormalized volume for asymptotically hyperbolic manifolds and prove a sharp Penrosetype inequality where mass is replaced by renormalized volume. Secondly, we use the notion of renormalized volume to study isoperimetric regions in asymptotically hyperbolic manifolds. We prove that for initial data sets that are Schwarzschildantide Sitter at infinity and satisfy appropriate scalar curvature lower bounds, sufficiently large coordinate spheres are uniquely isoperimetric. This is relevant in the context of Bray's isoperimetric approach to the Penrose inequality. From a geometric viewpoint, our results show that the largescale geometry of asymptotically hyperbolic manifolds significantly differs from the more familiar asymptotically flat setting. The renormalized volume is a very different quantity from the ``mass, '' and our results suggest that it is a stronger quantity. As a consequence of this, we uncover a link between scalar curvature and the behavior of large isoperimetric regions, which is not present in the asymptotically flat setting. Additionally, we discuss isoperimetric regions in warped products and consequences for the renormalized volume of a more general class of metrics. Finally, we study rotational symmetry of expanding Ricci solitons, a problem that is formally similar to the static uniqueness question with negative cosmological constant
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Related Identities
 Yau, ShingTung 1949 Editor
 Cao, HuaiDong Editor
 Vafa, Cumrun Contributor
 Kollár, János Contributor
 Cecottie, Sergio Contributor
 Wang, MuTao Contributor
 Zelditch, Steven 1953 Contributor
 Harvey, F. Reese Contributor
 Lawson, H. Blaine Contributor
 LeBrun, Claude 1956 Contributor
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Brendle, S.
Simon Brendle deutscher Mathematiker
Simon Brendle Duits wiskundige
Simon Brendle German mathematician
Simon Brendle matemàtic alemany
Simon Brendle matemático alemán
Simon Brendle mathématicien allemand
Simon Brendle tysk matematikar
Simon Brendle tysk matematiker
西蒙·布倫德
西蒙·布伦德勒
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