Hildebrandt, Stefan
Overview
Works:  186 works in 578 publications in 6 languages and 7,634 library holdings 

Genres:  Conference proceedings History 
Roles:  Author, Editor, Honoree, Contributor 
Classifications:  BH301.N3, 117 
Publication Timeline
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Most widely held works by
Stefan Hildebrandt
Mathematics and optimal form by
Stefan Hildebrandt(
Book
)
26 editions published between 1984 and 1998 in 4 languages and held by 1,452 WorldCat member libraries worldwide
Studie over de vraag waarom de natuur bepaalde vormen, zoals kristalvormen, prefereert boven vele andere mathematisch mogelijke vormen
26 editions published between 1984 and 1998 in 4 languages and held by 1,452 WorldCat member libraries worldwide
Studie over de vraag waarom de natuur bepaalde vormen, zoals kristalvormen, prefereert boven vele andere mathematisch mogelijke vormen
The parsimonious universe : shape and form in the natural world by
Stefan Hildebrandt(
Book
)
18 editions published between 1995 and 2013 in English and German and held by 754 WorldCat member libraries worldwide
Can one set of basic laws account for both the recurring themes and the infinite variety of nature's designs? When it comes to shape and form, does nature simply proceed in the easiest, most efficient way? Complete answers to these questions are likely never to be discovered. Still, down through the ages, the investigation of symmetry and regularity in nature has yielded some fascinating and surprising insights. Out of this inquiry comes a specific branch of mathematics  the calculus of variations  which explores questions of optimization: Is the igloo the optimal housing form for minimizing heat loss? Do bees use the least possible amount of wax when building their hives? In The Parsimonious Universe, Stefan Hildebrandt and Anthony Tromba invite readers to join the search for the mathematical underpinnings of natural shapes and form. Moving from ancient times to the nuclear age, the book looks at centuries of evidence that the physical world adheres to the principle of the economy of means  meaning that nature achieves efficiency by being rather stingy with the energy it expends. On almost every page can be found historical discussions, striking color illustrations, and examples ranging from atomic nuclei to soap bubbles to spirals and fractals. Without using technical language, Hildebrandt and Tromba open up an intriguing avenue of scientific inquiry to an uninitiated readership, showing what can be discovered when mathematics is used to investigate the natural world
18 editions published between 1995 and 2013 in English and German and held by 754 WorldCat member libraries worldwide
Can one set of basic laws account for both the recurring themes and the infinite variety of nature's designs? When it comes to shape and form, does nature simply proceed in the easiest, most efficient way? Complete answers to these questions are likely never to be discovered. Still, down through the ages, the investigation of symmetry and regularity in nature has yielded some fascinating and surprising insights. Out of this inquiry comes a specific branch of mathematics  the calculus of variations  which explores questions of optimization: Is the igloo the optimal housing form for minimizing heat loss? Do bees use the least possible amount of wax when building their hives? In The Parsimonious Universe, Stefan Hildebrandt and Anthony Tromba invite readers to join the search for the mathematical underpinnings of natural shapes and form. Moving from ancient times to the nuclear age, the book looks at centuries of evidence that the physical world adheres to the principle of the economy of means  meaning that nature achieves efficiency by being rather stingy with the energy it expends. On almost every page can be found historical discussions, striking color illustrations, and examples ranging from atomic nuclei to soap bubbles to spirals and fractals. Without using technical language, Hildebrandt and Tromba open up an intriguing avenue of scientific inquiry to an uninitiated readership, showing what can be discovered when mathematics is used to investigate the natural world
Partial differential equations and calculus of variations by
Stefan Hildebrandt(
Book
)
18 editions published in 1988 in English and held by 408 WorldCat member libraries worldwide
Annotation
18 editions published in 1988 in English and held by 408 WorldCat member libraries worldwide
Annotation
Calculus of variations and partial differential equations : proceedings of a conference held in Trento, Italy, June 1621,
1986 by
Stefan Hildebrandt(
Book
)
16 editions published in 1988 in English and held by 376 WorldCat member libraries worldwide
16 editions published in 1988 in English and held by 376 WorldCat member libraries worldwide
Calculus of variations by
Mariano Giaquinta(
Book
)
15 editions published between 1995 and 2004 in 3 languages and held by 349 WorldCat member libraries worldwide
15 editions published between 1995 and 2004 in 3 languages and held by 349 WorldCat member libraries worldwide
Calculus of variations and geometric evolution problems : lectures given at the 2nd session of the Centro Internazionale Matematico
Estivo (C.I.M.E.) held in Cetraro, Italy, June 1522, 1996 by
Fabrice Bethuel(
Book
)
17 editions published in 1999 in English and held by 277 WorldCat member libraries worldwide
The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for GinzburgLandau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds  both from the classical point of view and in the setting of geometric measure theory
17 editions published in 1999 in English and held by 277 WorldCat member libraries worldwide
The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for GinzburgLandau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds  both from the classical point of view and in the setting of geometric measure theory
Onedimensional variational problems : an introduction by
Giuseppe Buttazzo(
Book
)
15 editions published between 1998 and 2010 in English and Russian and held by 266 WorldCat member libraries worldwide
15 editions published between 1998 and 2010 in English and Russian and held by 266 WorldCat member libraries worldwide
Minimal surfaces by
Ulrich Dierkes(
Book
)
25 editions published between 1992 and 2013 in English and held by 202 WorldCat member libraries worldwide
"Minimal Surfaces" is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in threedimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently
25 editions published between 1992 and 2013 in English and held by 202 WorldCat member libraries worldwide
"Minimal Surfaces" is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in threedimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently
Geometric analysis and nonlinear partial differential equations by
Stefan Hildebrandt(
Book
)
9 editions published between 2002 and 2013 in English and held by 201 WorldCat member libraries worldwide
This wellorganized and coherent collection of papers leads the reader to the frontiers of present research in the theory of nonlinear partial differential equations and the calculus of variations and offers insight into some exciting developments. In addition, most articles also provide an excellent introduction to their background, describing extensively as they do the history of those problems presented, as well as the state of the art and offer a wellchosen guide to the literature. Part I contains the contributions of geometric nature: From spectral theory on regular and singular spaces to regularity theory of solutions of variational problems. Part II consists of articles on partial differential equations which originate from problems in physics, biology and stochastics. They cover elliptic, hyperbolic and parabolic cases
9 editions published between 2002 and 2013 in English and held by 201 WorldCat member libraries worldwide
This wellorganized and coherent collection of papers leads the reader to the frontiers of present research in the theory of nonlinear partial differential equations and the calculus of variations and offers insight into some exciting developments. In addition, most articles also provide an excellent introduction to their background, describing extensively as they do the history of those problems presented, as well as the state of the art and offer a wellchosen guide to the literature. Part I contains the contributions of geometric nature: From spectral theory on regular and singular spaces to regularity theory of solutions of variational problems. Part II consists of articles on partial differential equations which originate from problems in physics, biology and stochastics. They cover elliptic, hyperbolic and parabolic cases
Regularity of minimal surfaces by
Ulrich Dierkes(
Book
)
20 editions published between 2010 and 2013 in English and held by 133 WorldCat member libraries worldwide
"Regularity of Minimal Surfaces" begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and Hsurfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general GaussBonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is t
20 editions published between 2010 and 2013 in English and held by 133 WorldCat member libraries worldwide
"Regularity of Minimal Surfaces" begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and Hsurfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general GaussBonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is t
Global analysis of minimal surfaces by
Ulrich Dierkes(
Book
)
21 editions published between 2010 and 2013 in English and held by 128 WorldCat member libraries worldwide
Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of 'edgecrawling' along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional. In particular, far reaching Bernstein theorems are derived. The second part of the book contains what one might justly call a 'global theory of minimal surfaces' as envisioned by Smale. First, the Douglas problem is treated anew by using Teichmuller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau's problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented
21 editions published between 2010 and 2013 in English and held by 128 WorldCat member libraries worldwide
Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of 'edgecrawling' along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional. In particular, far reaching Bernstein theorems are derived. The second part of the book contains what one might justly call a 'global theory of minimal surfaces' as envisioned by Smale. First, the Douglas problem is treated anew by using Teichmuller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau's problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented
Wahrheit und Wert mathematischer Erkenntnis : Vortrag gehalten in der Carl Friedrich von Siemens Stiftung am 6. Februar 1992 by
Stefan Hildebrandt(
Book
)
4 editions published in 1995 in German and held by 114 WorldCat member libraries worldwide
4 editions published in 1995 in German and held by 114 WorldCat member libraries worldwide
Analysis by
Stefan Hildebrandt(
Book
)
6 editions published between 2002 and 2006 in German and held by 104 WorldCat member libraries worldwide
6 editions published between 2002 and 2006 in German and held by 104 WorldCat member libraries worldwide
The Hamiltonian formalism : Mariano Giaquinta ; Stefan Hildebrandt by
Mariano Giaquinta(
Book
)
23 editions published between 1996 and 2011 in English and Undetermined and held by 83 WorldCat member libraries worldwide
23 editions published between 1996 and 2011 in English and Undetermined and held by 83 WorldCat member libraries worldwide
Geometric analysis and the calculus of variations : for Stefan Hildebrandt(
Book
)
8 editions published in 1996 in English and held by 82 WorldCat member libraries worldwide
8 editions published in 1996 in English and held by 82 WorldCat member libraries worldwide
Analysis by
Stefan Hildebrandt(
Book
)
4 editions published between 2002 and 2007 in German and held by 59 WorldCat member libraries worldwide
4 editions published between 2002 and 2007 in German and held by 59 WorldCat member libraries worldwide
On onetoone harmonic mappings and minimal surfaces by
Stefan Hildebrandt(
Book
)
6 editions published between 1991 and 1992 in English and German and held by 55 WorldCat member libraries worldwide
6 editions published between 1991 and 1992 in English and German and held by 55 WorldCat member libraries worldwide
Otto Toeplitz by
Stefan Hildebrandt(
Book
)
8 editions published between 1950 and 1999 in German and English and held by 50 WorldCat member libraries worldwide
8 editions published between 1950 and 1999 in German and English and held by 50 WorldCat member libraries worldwide
Analysis 1 by
Stefan Hildebrandt(
Book
)
2 editions published between 2006 and 2007 in German and held by 1 WorldCat member library worldwide
2 editions published between 2006 and 2007 in German and held by 1 WorldCat member library worldwide
Felix Hausdorff Gesammelte Werke by
Josef Bemelmans(
)
2 editions published in 2006 in German and held by 0 WorldCat member libraries worldwide
Band 5 umfabt die Themenbereiche Astronomie, Optik und Wahrscheinlichkeitstheorie. Er enthalt Hausdorffs Dissertation uber die Refraktion des Lichtes in der Atmosphare, zwei Folgearbeiten zum gleichen Thema sowie die Habilitationsschrift uber die Extinktion des Lichtes in der Atmosphare. Es folgt eine Arbeit uber geometrische Optik
2 editions published in 2006 in German and held by 0 WorldCat member libraries worldwide
Band 5 umfabt die Themenbereiche Astronomie, Optik und Wahrscheinlichkeitstheorie. Er enthalt Hausdorffs Dissertation uber die Refraktion des Lichtes in der Atmosphare, zwei Folgearbeiten zum gleichen Thema sowie die Habilitationsschrift uber die Extinktion des Lichtes in der Atmosphare. Es folgt eine Arbeit uber geometrische Optik
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Related Identities
 Tromba, Anthony
 Dierkes, Ulrich Author
 Giaquinta, Mariano 1947 Author
 Sauvigny, Friedrich
 Leis, Rolf Editor
 Küster, Albrecht Contributor
 Kinderlehrer, David Editor
 Miranda, Mario 1937 Editor
 Bethuel, Fabrice 1963 Author
 Jakob, Ruben Contributor
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Associated Subjects
Astronomy Boundary value problems Calculus Calculus of variations Differential equations, Elliptic Differential equations, Nonlinear Differential equations, Partial Distribution (Probability theory) Form (Philosophy) Forms (Mathematics) Functions of complex variables Geometry, Differential Global analysis (Mathematics) Global differential geometry Hamiltonian systems Harmonic maps Hypersurfaces Mathematical analysis Mathematical optimization Mathematical physics Mathematics Mathematics in nature Minimal surfaces Motion Nature (Aesthetics) Physical optics Physics Riemannian manifolds Statistics Toeplitz, Otto, Toeplitz operators
Alternative Names
Hildebrandt, S.
Hildebrandt, S. 1936
Hildebrandt, S. (Stefan)
Hildebrandt, St. 1936
Hildebrandt, Stefan
Hildebrandt, Stephan 1936
Hilderbrandt, S.
Hilderbrandt, S. (Stefan)
Stefan Hildebrandt deutscher Mathematiker
Stefan Hildebrandt tysk matematikar
Stefan Hildebrandt tysk matematiker
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