Ballmann, Werner
Overview
Works:  41 works in 116 publications in 4 languages and 1,444 library holdings 

Roles:  Author, Editor, Thesis advisor 
Classifications:  QA649, 516.36 
Publication Timeline
.
Most widely held works by
Werner Ballmann
Manifolds of nonpositive curvature by
Werner Ballmann(
Book
)
18 editions published between 1985 and 2013 in 3 languages and held by 350 WorldCat member libraries worldwide
This volume presents a complete and selfcontained description of new results in the theory of manifolds of nonpositive curvature. It is based on lectures delivered by M. Gromov at the Collge de France in Paris. Among others these lectures threat local and global rigidity problems (e.g., a generalization of the famous Mostow rigidity theorem) and finiteness results for manifolds of finite volume. V. Schroeder wrote up these lectures, including complete and detailed proofs. A lot of background material is added to the first lectures. Therefore this book may also serve as an introduction to the subject of nonpositively curved manifolds. The latest progress in this area is reflected in the article of W. Ballmann describing the structure of manifolds of higher rank
18 editions published between 1985 and 2013 in 3 languages and held by 350 WorldCat member libraries worldwide
This volume presents a complete and selfcontained description of new results in the theory of manifolds of nonpositive curvature. It is based on lectures delivered by M. Gromov at the Collge de France in Paris. Among others these lectures threat local and global rigidity problems (e.g., a generalization of the famous Mostow rigidity theorem) and finiteness results for manifolds of finite volume. V. Schroeder wrote up these lectures, including complete and detailed proofs. A lot of background material is added to the first lectures. Therefore this book may also serve as an introduction to the subject of nonpositively curved manifolds. The latest progress in this area is reflected in the article of W. Ballmann describing the structure of manifolds of higher rank
Lectures on spaces of nonpositive curvature by
Werner Ballmann(
Book
)
16 editions published in 1995 in 3 languages and held by 265 WorldCat member libraries worldwide
Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the HadamardCartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a selfcontained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the nonspecialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory
16 editions published in 1995 in 3 languages and held by 265 WorldCat member libraries worldwide
Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the HadamardCartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a selfcontained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the nonspecialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory
Lectures on Kähler manifolds by
Werner Ballmann(
Book
)
13 editions published in 2006 in English and held by 213 WorldCat member libraries worldwide
These notes are based on lectures the author held at the University of Bonn and the ErwinSchrödingerInstitute in Vienna. The aim is to give a thorough introduction to the theory of Kähler manifolds with special emphasis on the differential geometric side of Kähler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kähler manifolds. The more advanced topics are the cohomology of Kähler manifolds, Calabi conjecture, Gromov's Kähler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on ChernWeil theory, symmetric spaces, and L2cohomology
13 editions published in 2006 in English and held by 213 WorldCat member libraries worldwide
These notes are based on lectures the author held at the University of Bonn and the ErwinSchrödingerInstitute in Vienna. The aim is to give a thorough introduction to the theory of Kähler manifolds with special emphasis on the differential geometric side of Kähler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kähler manifolds. The more advanced topics are the cohomology of Kähler manifolds, Calabi conjecture, Gromov's Kähler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on ChernWeil theory, symmetric spaces, and L2cohomology
Einführung in die Geometrie und Topologie by
Werner Ballmann(
)
7 editions published in 2015 in German and held by 70 WorldCat member libraries worldwide
Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der JordanBrouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein oder zweisemestrige Vorlesungen geeignet
7 editions published in 2015 in German and held by 70 WorldCat member libraries worldwide
Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der JordanBrouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein oder zweisemestrige Vorlesungen geeignet
Der Satz von Lusternik und Schnirelmann by
Werner Ballmann(
Book
)
7 editions published in 1978 in 3 languages and held by 67 WorldCat member libraries worldwide
7 editions published in 1978 in 3 languages and held by 67 WorldCat member libraries worldwide
Arbeitstagung Bonn 2013 : in memory of Friedrich Hirzebruch by
Werner Ballmann(
Book
)
9 editions published in 2016 in English and held by 43 WorldCat member libraries worldwide
This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 2228. The 2013 meeting (and this resulting proceedings) was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion. This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung. (4e de couv.)
9 editions published in 2016 in English and held by 43 WorldCat member libraries worldwide
This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 2228. The 2013 meeting (and this resulting proceedings) was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion. This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung. (4e de couv.)
Der Hafen Oldenburg : Entwicklung und Struktur, Bedeutung und Verflechtung by
Werner Ballmann(
Book
)
7 editions published in 1976 in German and held by 40 WorldCat member libraries worldwide
7 editions published in 1976 in German and held by 40 WorldCat member libraries worldwide
Beitrag zur Klärung des betriebswirtschaftlichen Investitionsbegriffes und zur Entwicklung einer Investitionspolitik der
Unternehmung by
Werner Ballmann(
Book
)
3 editions published in 1954 in German and held by 27 WorldCat member libraries worldwide
3 editions published in 1954 in German and held by 27 WorldCat member libraries worldwide
Einige neue Resultate über Mannigfaltigkeiten nicht positiver Krümmung by
Werner Ballmann(
Book
)
1 edition published in 1978 in German and held by 7 WorldCat member libraries worldwide
1 edition published in 1978 in German and held by 7 WorldCat member libraries worldwide
Crystalline Dieudonné module theory via formal and rigid geometry by
A. J. de Jong(
Book
)
1 edition published in 1996 in French and held by 5 WorldCat member libraries worldwide
1 edition published in 1996 in French and held by 5 WorldCat member libraries worldwide
An estimate for the measure theoretic entropy of geodesic flows by
Werner Ballmann(
Book
)
2 editions published in 1987 in German and English and held by 4 WorldCat member libraries worldwide
2 editions published in 1987 in German and English and held by 4 WorldCat member libraries worldwide
Differentialgeometrie im Großen : 08.06.  14.06.1997(
Book
)
2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
The Martin boundary of certain Hadamard manifolds by
Werner Ballmann(
Book
)
2 editions published in 1990 in German and English and held by 4 WorldCat member libraries worldwide
2 editions published in 1990 in German and English and held by 4 WorldCat member libraries worldwide
Differentialgeometrie im Großen : June 10th  June 16th, 2001(
Book
)
1 edition published in 2001 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 4 WorldCat member libraries worldwide
Geometric rigidity and hyperbolic dynamics : 18. February  24. February, 2001(
Book
)
1 edition published in 2001 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 4 WorldCat member libraries worldwide
Manifolds of Nonpositive Curvature by
Werner Ballmann(
)
1 edition published in 1985 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1985 in English and held by 3 WorldCat member libraries worldwide
Méthodes spinorielles et géométrie paracomplexe et paraquaternionique en théorie des sousvariétés by
MarieAmélie PaillusseauLawn(
Book
)
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
This thesis is devoted to the theory of immersions, using methods of spin geometry, paracomplex and paraquaternionic geometry. It is subdivided into three different topics. The first two are related to the study of conformal immersions of pseudoRiemannian surfaces. On the one hand we study the immersion into threedimensional pseudoEuclidean spaces: with the methods of paracomplex geometry and using real spinor representations, we prove the equivalence between the data of a conformal immersion of a Lorentzian surface in R2,1 and spinors satisfying a Diractype equation. On the other hand, we consider immersions of such surfaces into the fourdimensional pseudosphere S2,2: a onetoone correspondence between such immersions and paraquaternionic line subbundles of the trivial bundle M X H2 is given. Considering a particular (para)complex structure on this bundle, namely the mean curvature pseudosphere congruence, and the paraquaternionic Hopf fields of the immersion, we define the Willmore functional of the surface and can express its energy as the sum of this functional and of a topological invariant. The last topic is more general and deals with paracomplex vector bundles and paracomplex affine immersions. We introduce paraholomorphic vector bundles and characterize paraholomorphic subbundles and subbundles of type (1,1) in terms of the associated induced connections and second fundamental forms. The fundamental equations for general decompositions of vector bundles with connection are studied in the case where some of the (sub)bundle are paraholomorphic in order to prove existence and uniqueness theorems of paracomplex affine immersions
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
This thesis is devoted to the theory of immersions, using methods of spin geometry, paracomplex and paraquaternionic geometry. It is subdivided into three different topics. The first two are related to the study of conformal immersions of pseudoRiemannian surfaces. On the one hand we study the immersion into threedimensional pseudoEuclidean spaces: with the methods of paracomplex geometry and using real spinor representations, we prove the equivalence between the data of a conformal immersion of a Lorentzian surface in R2,1 and spinors satisfying a Diractype equation. On the other hand, we consider immersions of such surfaces into the fourdimensional pseudosphere S2,2: a onetoone correspondence between such immersions and paraquaternionic line subbundles of the trivial bundle M X H2 is given. Considering a particular (para)complex structure on this bundle, namely the mean curvature pseudosphere congruence, and the paraquaternionic Hopf fields of the immersion, we define the Willmore functional of the surface and can express its energy as the sum of this functional and of a topological invariant. The last topic is more general and deals with paracomplex vector bundles and paracomplex affine immersions. We introduce paraholomorphic vector bundles and characterize paraholomorphic subbundles and subbundles of type (1,1) in terms of the associated induced connections and second fundamental forms. The fundamental equations for general decompositions of vector bundles with connection are studied in the case where some of the (sub)bundle are paraholomorphic in order to prove existence and uniqueness theorems of paracomplex affine immersions
Beitrag zur Klärung des betriebwirtschaftlichen Investitionsbegriffes und zur Entwicklung einer Investitionspolitik der Unternehmung by
Werner Ballmann(
Book
)
1 edition published in 1954 in German and held by 2 WorldCat member libraries worldwide
1 edition published in 1954 in German and held by 2 WorldCat member libraries worldwide
Boundary value problems for elliptic differential operators of first order by
Christian Bär(
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncom pact, but the boundary is assumed to be compact.We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regurality of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson’s relative index theorem and a generalization of the cobordism theorem
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncom pact, but the boundary is assumed to be compact.We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regurality of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson’s relative index theorem and a generalization of the cobordism theorem
Géométrie tt* et applications pluriharmoniques by
Lars Schäfer(
Book
)
1 edition published in 2006 in French and held by 1 WorldCat member library worldwide
In this work we introduce the real differential geometric notion of a tt*bundle (E,D,S), a metric tt*bundle (E,D,S,g) and a symplectic tt*bundle (E,D,S,omega) on an abstract vector bundle E over an almost complex manifold (M,J). With this notion we construct, generalizing Dubrovin, a correspondence between metric tt*bundles over complex manifolds (M,J) and admissible pluriharmonic maps from (M,J) into the pseudoRiemannian symmetric space GL(r,R)/O(p,q) where (p,q) is the signature of the metric g. Moreover, we show a rigidity result for tt*bundles over compact Kähler manifolds and we obtain as application a special case of Lu's theorem. In addition we study solutions of tt*bundles (TM,D,S) on the tangent bundle TM of (M,J) and characterize an interesting class of these solutions which contains special complex manifolds and flat nearly Kähler manifolds. We analyze which elements of this class admit metric or symplectic tt*bundles. Further we consider solutions coming from varitations of Hodge structures (VHS) and harmonic bundles. Applying our correspondence to harmonic bundles we generalize a correspondence given by Simpson. Analyzing the associated pluriharmonic maps we obtain roughly speaking for special Kähler manifolds the dual Gauss map and for VHS of odd weight the period map. In the case of nonintegrable complex structures, we need to generalize the notions of pluriharmonic maps and some results. Apart from the rigidity result we generalize all above results to paracomplex geometry
1 edition published in 2006 in French and held by 1 WorldCat member library worldwide
In this work we introduce the real differential geometric notion of a tt*bundle (E,D,S), a metric tt*bundle (E,D,S,g) and a symplectic tt*bundle (E,D,S,omega) on an abstract vector bundle E over an almost complex manifold (M,J). With this notion we construct, generalizing Dubrovin, a correspondence between metric tt*bundles over complex manifolds (M,J) and admissible pluriharmonic maps from (M,J) into the pseudoRiemannian symmetric space GL(r,R)/O(p,q) where (p,q) is the signature of the metric g. Moreover, we show a rigidity result for tt*bundles over compact Kähler manifolds and we obtain as application a special case of Lu's theorem. In addition we study solutions of tt*bundles (TM,D,S) on the tangent bundle TM of (M,J) and characterize an interesting class of these solutions which contains special complex manifolds and flat nearly Kähler manifolds. We analyze which elements of this class admit metric or symplectic tt*bundles. Further we consider solutions coming from varitations of Hodge structures (VHS) and harmonic bundles. Applying our correspondence to harmonic bundles we generalize a correspondence given by Simpson. Analyzing the associated pluriharmonic maps we obtain roughly speaking for special Kähler manifolds the dual Gauss map and for VHS of odd weight the period map. In the case of nonintegrable complex structures, we need to generalize the notions of pluriharmonic maps and some results. Apart from the rigidity result we generalize all above results to paracomplex geometry
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Related Identities
 Schroeder, Viktor
 Gromov, Mikhael 1943
 Hirzebruch, Friedrich Dedicatee
 Blohmann, Christian Editor
 Brin, Misha Other Writer of accompanying material
 Faltings, Gerd Editor
 Teichner, Peter Editor
 Matthias, HansHeinrich
 Zagier, Don Editor
 European Mathematical Society Publisher
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Associated Subjects
Algebraic topology Cell aggregationMathematics Curvature Curves, Algebraic Discrete groups Flows (Differentiable dynamical systems) Geodesic flows Geometry Geometry, Algebraic Geometry, Differential Germany GermanyGronau (North RhineWestphalia) GermanyOldenburg Global analysis (Mathematics) Global differential geometry Group theory Hirzebruch, Friedrich Homology theory Homomorphisms (Mathematics) Isometrics (Mathematics) Kählerian manifolds Lattice theory Manifolds (Mathematics) Mathematicians Mathematics Metric spaces Operator theory Riemannian manifolds Semisimple Lie groups Topological groups Topological transformation groups Topology
Alternative Names
Ballmann, Hans Werner 1951
Ballmann, W. 1951
Ballmann, Werner
Hans Werner Ballmann Duits wiskundige
Hans Werner Ballmann German mathematician
Hans Werner Ballmann mathématicien allemand
Werner Ballmann deutscher Mathematiker
Werner Ballmann tysk matematikar
Werner Ballmann tysk matematiker
Балманн, Вернер
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