Hildebrandt, Stefan
Overview
Works:  158 works in 623 publications in 5 languages and 8,044 library holdings 

Genres:  Conference papers and proceedings History 
Roles:  Author, Editor, Honoree, Other, Contributor, Creator 
Classifications:  BH301.N3, 117 
Publication Timeline
.
Most widely held works by
Stefan Hildebrandt
Mathematics and optimal form by
Stefan Hildebrandt(
Book
)
30 editions published between 1984 and 1998 in 5 languages and held by 1,454 WorldCat member libraries worldwide
The authors look at familiar examples of nature's tendency to economize, to the nuclei of atoms to the planets of our solar system
30 editions published between 1984 and 1998 in 5 languages and held by 1,454 WorldCat member libraries worldwide
The authors look at familiar examples of nature's tendency to economize, to the nuclei of atoms to the planets of our solar system
The parsimonious universe : shape and form in the natural world by
Stefan Hildebrandt(
Book
)
20 editions published between 1995 and 2013 in English and German and held by 767 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
20 editions published between 1995 and 2013 in English and German and held by 767 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
Calculus of variations by
Mariano Giaquinta(
Book
)
73 editions published between 1994 and 2011 in English and Undetermined and held by 602 WorldCat member libraries worldwide
This longawaited book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins, partly in applications, e.g. from geometrical optics, of parts of the theory. A variety of aids to the reader are provided: besides the very detailed table of contents, an introduction to each chapter, section and subsection, an overview of the relevant literature (in Vol. 2) plus the references in the Scholia to each chapter, in the (historical) footnotes, and in the bibliography, and finally an index of the examples used throughout the book. Both individually and collectively these volumes have already become standard references
73 editions published between 1994 and 2011 in English and Undetermined and held by 602 WorldCat member libraries worldwide
This longawaited book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins, partly in applications, e.g. from geometrical optics, of parts of the theory. A variety of aids to the reader are provided: besides the very detailed table of contents, an introduction to each chapter, section and subsection, an overview of the relevant literature (in Vol. 2) plus the references in the Scholia to each chapter, in the (historical) footnotes, and in the bibliography, and finally an index of the examples used throughout the book. Both individually and collectively these volumes have already become standard references
Partial differential equations and calculus of variations by
Stefan Hildebrandt(
Book
)
18 editions published in 1988 in English and Undetermined and held by 386 WorldCat member libraries worldwide
This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory
18 editions published in 1988 in English and Undetermined and held by 386 WorldCat member libraries worldwide
This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory
Calculus of variations and partial differential equations : proceedings of a conference held in Trento, Italy, June 1621,
1986 by
Stefan Hildebrandt(
Book
)
17 editions published in 1988 in English and Undetermined and held by 351 WorldCat member libraries worldwide
Annotation
17 editions published in 1988 in English and Undetermined and held by 351 WorldCat member libraries worldwide
Annotation
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
)
27 editions published in 1999 in English and German and held by 334 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
27 editions published in 1999 in English and German and held by 334 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
Minimal surfaces by
Ulrich Dierkes(
Book
)
54 editions published between 1992 and 2013 in English and German and held by 298 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
54 editions published between 1992 and 2013 in English and German and held by 298 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
Onedimensional variational problems : an introduction by
Giuseppe Buttazzo(
Book
)
15 editions published between 1998 and 2010 in English and Russian and held by 278 WorldCat member libraries worldwide
While easier to solve and accessible to a broader range of students, onedimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higherdimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory
15 editions published between 1998 and 2010 in English and Russian and held by 278 WorldCat member libraries worldwide
While easier to solve and accessible to a broader range of students, onedimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higherdimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory
Geometric analysis and nonlinear partial differential equations by
Stefan Hildebrandt(
Book
)
12 editions published between 2002 and 2013 in English and held by 210 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
12 editions published between 2002 and 2013 in English and held by 210 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
Wahrheit und Wert mathematischer Erkenntnis : Vortrag gehalten in der Carl Friedrich von Siemens Stiftung am 6. Februar 1992 by
Stefan Hildebrandt(
Book
)
14 editions published in 1995 in German and held by 156 WorldCat member libraries worldwide
14 editions published in 1995 in German and held by 156 WorldCat member libraries worldwide
Minimal surfaces by
Ulrich Dierkes(
Book
)
13 editions published in 2010 in English and held by 125 WorldCat member libraries worldwide
13 editions published in 2010 in English and held by 125 WorldCat member libraries worldwide
Analysis by
Stefan Hildebrandt(
Book
)
8 editions published between 2002 and 2006 in German and held by 115 WorldCat member libraries worldwide
8 editions published between 2002 and 2006 in German and held by 115 WorldCat member libraries worldwide
Geometric analysis and the calculus of variations : for Stefan Hildebrandt(
Book
)
9 editions published in 1996 in English and held by 86 WorldCat member libraries worldwide
9 editions published in 1996 in English and held by 86 WorldCat member libraries worldwide
Analysis by
Stefan Hildebrandt(
Book
)
6 editions published between 2002 and 2008 in German and held by 81 WorldCat member libraries worldwide
Der zweite Band dieses Lehrbuchs der Analysis umfaßt den Stoff des zweiten Semesters eines mathematischen Grundstudiums für Studierende der Mathematik, Physik und Informatik. Der klare und übersichtliche Aufbau berücksichtigt, daß schon frühzeitig die mathematischen Hilfsmittel erörtert werden, die zum Verständnis der physikalischen Grundvorlesungen unerläßlich sind. In Verbindung mit Band 1 ist so ein Leitfaden für das Studium der Analysis entstanden, der das in den ersten beiden Studiensemestern zu erwerbende mathematische Grundwissen umfaßt. Ausführliche Beweise und Erläuterungen sowie zahlreiche Beispiele und interessante Übungsaufgaben eignen es sehr gut für das Selbststudium. Ein klarer und übersichtlicher Aufbau und eine geschickte Gliederung des Stoffes ermöglichen, das erste Studium auf Kernbereiche zu beschränken. Geometrische Intuition und historische Motivation in Verbindung mit einer maßvollen Abstraktion kennzeichnen diese moderne Einführung in die Analysis
6 editions published between 2002 and 2008 in German and held by 81 WorldCat member libraries worldwide
Der zweite Band dieses Lehrbuchs der Analysis umfaßt den Stoff des zweiten Semesters eines mathematischen Grundstudiums für Studierende der Mathematik, Physik und Informatik. Der klare und übersichtliche Aufbau berücksichtigt, daß schon frühzeitig die mathematischen Hilfsmittel erörtert werden, die zum Verständnis der physikalischen Grundvorlesungen unerläßlich sind. In Verbindung mit Band 1 ist so ein Leitfaden für das Studium der Analysis entstanden, der das in den ersten beiden Studiensemestern zu erwerbende mathematische Grundwissen umfaßt. Ausführliche Beweise und Erläuterungen sowie zahlreiche Beispiele und interessante Übungsaufgaben eignen es sehr gut für das Selbststudium. Ein klarer und übersichtlicher Aufbau und eine geschickte Gliederung des Stoffes ermöglichen, das erste Studium auf Kernbereiche zu beschränken. Geometrische Intuition und historische Motivation in Verbindung mit einer maßvollen Abstraktion kennzeichnen diese moderne Einführung in die Analysis
Calculus of Variations and Partial Differential Equations : Proceedings of a Conference held in Trento, Italy June 1621,
1986 by
Stefan Hildebrandt(
)
4 editions published in 1988 in English and held by 76 WorldCat member libraries worldwide
4 editions published in 1988 in English and held by 76 WorldCat member libraries worldwide
Otto Toeplitz by
Stefan Hildebrandt(
Book
)
9 editions published between 1950 and 1999 in German and English and held by 57 WorldCat member libraries worldwide
Presents a brief biographical sketch of Jewish German mathematician Otto Toeplitz (18811940), compiled as part of the MacTutor History of Mathematics Archive of the School of Mathematics and Statistics at the University of Saint Andrews in Scotland. Notes that Toeplitz's work focused on infinite linear and quadratic forms
9 editions published between 1950 and 1999 in German and English and held by 57 WorldCat member libraries worldwide
Presents a brief biographical sketch of Jewish German mathematician Otto Toeplitz (18811940), compiled as part of the MacTutor History of Mathematics Archive of the School of Mathematics and Statistics at the University of Saint Andrews in Scotland. Notes that Toeplitz's work focused on infinite linear and quadratic forms
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 57 WorldCat member libraries worldwide
6 editions published between 1991 and 1992 in English and German and held by 57 WorldCat member libraries worldwide
Felix Hausdorff Gesammelte Werke by
Josef Bemelmans(
)
4 editions published in 2006 in German and English and held by 0 WorldCat member libraries worldwide
Band 5 umfaßt die Themenbereiche Astronomie, Optik und Wahrscheinlichkeitstheorie. Er enthält Hausdorffs Dissertation über die Refraktion des Lichtes in der Atmosphäre, zwei Folgearbeiten zum gleichen Thema sowie die Habilitationsschrift über die Extinktion des Lichtes in der Atmosphäre. Es folgt eine Arbeit über geometrische Optik, die unmittelbar an die berühmte Publikation von H. Bruns über das Eikonal anschließt und in der Hausdorff die damals ganz neuen Lieschen Theorien für die Optik nutzbar zu machen suchte. Auf dem Gebiet der Stochastik veröffentlichte Hausdorff zwei längere Arbeiten, die in verschiedenen Bereichen der Versicherungsmathematik und der Wahrscheinlichkeitsrechnung ihre Spuren hinterlassen haben. Von besonderem historischen Interesse sind die im Band publizierten Stücke aus Hausdorffs Nachlaß, etwa seine Vorlesung "Wahrscheinlichkeitsrechnung" vom Sommersemester 1923 oder seine Briefe an Richard von Mises aus dem Jahre 1919
4 editions published in 2006 in German and English and held by 0 WorldCat member libraries worldwide
Band 5 umfaßt die Themenbereiche Astronomie, Optik und Wahrscheinlichkeitstheorie. Er enthält Hausdorffs Dissertation über die Refraktion des Lichtes in der Atmosphäre, zwei Folgearbeiten zum gleichen Thema sowie die Habilitationsschrift über die Extinktion des Lichtes in der Atmosphäre. Es folgt eine Arbeit über geometrische Optik, die unmittelbar an die berühmte Publikation von H. Bruns über das Eikonal anschließt und in der Hausdorff die damals ganz neuen Lieschen Theorien für die Optik nutzbar zu machen suchte. Auf dem Gebiet der Stochastik veröffentlichte Hausdorff zwei längere Arbeiten, die in verschiedenen Bereichen der Versicherungsmathematik und der Wahrscheinlichkeitsrechnung ihre Spuren hinterlassen haben. Von besonderem historischen Interesse sind die im Band publizierten Stücke aus Hausdorffs Nachlaß, etwa seine Vorlesung "Wahrscheinlichkeitsrechnung" vom Sommersemester 1923 oder seine Briefe an Richard von Mises aus dem Jahre 1919
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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 Other Author Editor
 Miranda, Mario 1937 Other Editor
 Bethuel, Fabrice 1963 Other Author
 Struwe, Michael 1955 Other Editor
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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 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. 19362015
Hildebrandt, S. (Stefan)
Hildebrandt, St. 19362015
Hildebrandt, Stefan
Hildebrandt, Stefan O. W.
Hildebrandt, Stephan 1936
Hildebrandt, Stephan 19362015
Hilderbrandt, S.
Hilderbrandt, S. (Stefan)
Stefan Hildebrandt deutscher Mathematiker
Stefan Hildebrandt Duits wiskundige (19362015)
Stefan Hildebrandt German mathematician
Stefan Hildebrandt tysk matematikar
Stefan Hildebrandt tysk matematiker
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