Tromba, Anthony
Overview
Works:  74 works in 449 publications in 8 languages and 7,732 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA303, 117 
Publication Timeline
.
Most widely held works by
Anthony Tromba
Vector calculus by
Jerrold E Marsden(
Book
)
127 editions published between 1970 and 2013 in 6 languages and held by 1,811 WorldCat member libraries worldwide
Now in its fifth edition, Vector Calculus helps students gain an intuitive and solid understanding of this important subject. The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world. (Midwest)
127 editions published between 1970 and 2013 in 6 languages and held by 1,811 WorldCat member libraries worldwide
Now in its fifth edition, Vector Calculus helps students gain an intuitive and solid understanding of this important subject. The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world. (Midwest)
Mathematics and optimal form by
Stefan Hildebrandt(
Book
)
26 editions published between 1984 and 1998 in 3 languages and held by 1,350 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
26 editions published between 1984 and 1998 in 3 languages and held by 1,350 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
)
17 editions published between 1995 and 1996 in English and German and held by 760 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
17 editions published between 1995 and 1996 in English and German and held by 760 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
Teichmüller theory in Riemannian geometry by
Anthony Tromba(
Book
)
17 editions published in 1992 in 3 languages and held by 304 WorldCat member libraries worldwide
These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 19801986. Since then many of our colleagues have encouraged us to publish our approach to the subject in a concise format, easily accessible to a broad mathematical audience. However, it was the invitation by the faculty of the ETH Ziirich to deliver the ETH N achdiplomVorlesungen on this material which provided the opportunity for the author to develop our research papers into a format suitable for mathematicians with a modest background in differential geometry. We also hoped it would provide the basis for a graduate course stressing the application of fundamental ideas in geometry. For this opportunity the author wishes to thank Eduard Zehnder and Jiirgen Moser, acting director and director of the Forschungsinstitut fiir Mathematik at the ETH, Gisbert Wiistholz, responsible for the Nachdiplom Vorlesungen and the entire ETH faculty for their support and warm hospitality. This new approach to Teichmiiller theory presented here was undertaken for two reasons. First, it was clear that the classical approach, using the theory of extremal quasiconformal mappings (in this approach we completely avoid the use of quasiconformal maps) was not easily applicable to the theory of minimal surfaces, a field of interest of the author over many years. Second, many other active mathematicians, who at various times needed some Teichmiiller theory, have found the classical approach inaccessible to them
17 editions published in 1992 in 3 languages and held by 304 WorldCat member libraries worldwide
These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 19801986. Since then many of our colleagues have encouraged us to publish our approach to the subject in a concise format, easily accessible to a broad mathematical audience. However, it was the invitation by the faculty of the ETH Ziirich to deliver the ETH N achdiplomVorlesungen on this material which provided the opportunity for the author to develop our research papers into a format suitable for mathematicians with a modest background in differential geometry. We also hoped it would provide the basis for a graduate course stressing the application of fundamental ideas in geometry. For this opportunity the author wishes to thank Eduard Zehnder and Jiirgen Moser, acting director and director of the Forschungsinstitut fiir Mathematik at the ETH, Gisbert Wiistholz, responsible for the Nachdiplom Vorlesungen and the entire ETH faculty for their support and warm hospitality. This new approach to Teichmiiller theory presented here was undertaken for two reasons. First, it was clear that the classical approach, using the theory of extremal quasiconformal mappings (in this approach we completely avoid the use of quasiconformal maps) was not easily applicable to the theory of minimal surfaces, a field of interest of the author over many years. Second, many other active mathematicians, who at various times needed some Teichmiiller theory, have found the classical approach inaccessible to them
Calculus by
Kenneth McAloon(
Book
)
5 editions published in 1972 in English and held by 239 WorldCat member libraries worldwide
Introductory course for students with a highschool background of algebra, geometry and rudiments of trigonometry
5 editions published in 1972 in English and held by 239 WorldCat member libraries worldwide
Introductory course for students with a highschool background of algebra, geometry and rudiments of trigonometry
Existence theorems for minimal surfaces of nonzero genus spanning a contour by
Friedrich Tomi(
Book
)
10 editions published in 1988 in English and held by 233 WorldCat member libraries worldwide
10 editions published in 1988 in English and held by 233 WorldCat member libraries worldwide
The index theorem for minimal surfaces of higher genus by
Friedrich Tomi(
Book
)
9 editions published in 1995 in English and held by 230 WorldCat member libraries worldwide
9 editions published in 1995 in English and held by 230 WorldCat member libraries worldwide
On the number of simply connected minimal surfaces spanning a curve by
Anthony Tromba(
Book
)
12 editions published in 1977 in English and held by 219 WorldCat member libraries worldwide
12 editions published in 1977 in English and held by 219 WorldCat member libraries worldwide
Basic multivariable calculus by
Jerrold E Marsden(
Book
)
21 editions published between 1993 and 2000 in 4 languages and held by 205 WorldCat member libraries worldwide
21 editions published between 1993 and 2000 in 4 languages and held by 205 WorldCat member libraries worldwide
Seminar on New Results in Nonlinear Partial Differential Equations : a publication of the MaxPlanckInstitut für Mathematik,
Bonn by
Anthony Tromba(
Book
)
20 editions published in 1987 in English and Undetermined and held by 183 WorldCat member libraries worldwide
Recent years have seen a tremendous growth of interest in nonlinear partial differential equations_ Yau's solution of the Calabi conjecture and more recently Schoen's solution of the Yamabe problem and Wente's counterexample of the Hopf conjecture have been a great stimulus to geometric P.D.E . Applied P.D.E. has also seen great progress. The "year" in P.D.E., JanuarySeptember 1984 at the MaxPlanckI nstitute was dedicated to bringing together some of the leaders in several fields of P.D.E . We preferred a seminar focused not on a given very specific area but one which cuts across boundaries of research interests. We hoped to have a snapshot of some of the more important recent devel opments in nonlinear P.D.E . The current volume contains some of the results reported upon in this seminar. From Henry Wente, in geometric P.D.E., we have new toroidal counterexamples to Hopf's conjecture, and, due to Uwe Abresch, a further development of these ideas. Sergiu Klainerman's global existence result for the nonlinear KleinGordon equation in four spacetime dimensions, achieved while at Max Planck, is included. Vince Moncrief presents his global existence result for the YangMills equation in Min kowski space time. All of these results answer important and outstanding questions
20 editions published in 1987 in English and Undetermined and held by 183 WorldCat member libraries worldwide
Recent years have seen a tremendous growth of interest in nonlinear partial differential equations_ Yau's solution of the Calabi conjecture and more recently Schoen's solution of the Yamabe problem and Wente's counterexample of the Hopf conjecture have been a great stimulus to geometric P.D.E . Applied P.D.E. has also seen great progress. The "year" in P.D.E., JanuarySeptember 1984 at the MaxPlanckI nstitute was dedicated to bringing together some of the leaders in several fields of P.D.E . We preferred a seminar focused not on a given very specific area but one which cuts across boundaries of research interests. We hoped to have a snapshot of some of the more important recent devel opments in nonlinear P.D.E . The current volume contains some of the results reported upon in this seminar. From Henry Wente, in geometric P.D.E., we have new toroidal counterexamples to Hopf's conjecture, and, due to Uwe Abresch, a further development of these ideas. Sergiu Klainerman's global existence result for the nonlinear KleinGordon equation in four spacetime dimensions, achieved while at Max Planck, is included. Vince Moncrief presents his global existence result for the YangMills equation in Min kowski space time. All of these results answer important and outstanding questions
Regularity of minimal surfaces by
Ulrich Dierkes(
Book
)
20 editions published between 2010 and 2013 in English and held by 139 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 139 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
)
22 editions published between 2010 and 2013 in English and held by 132 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
22 editions published between 2010 and 2013 in English and held by 132 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
Calculus of one variable by
Kenneth McAloon(
Book
)
5 editions published in 1972 in English and held by 131 WorldCat member libraries worldwide
5 editions published in 1972 in English and held by 131 WorldCat member libraries worldwide
Panoptimum : mathematische Grundmuster des Vollkommenen by
Stefan Hildebrandt(
Book
)
3 editions published in 1987 in German and held by 97 WorldCat member libraries worldwide
3 editions published in 1987 in German and held by 97 WorldCat member libraries worldwide
A theory of branched minimal surfaces by
Anthony Tromba(
Book
)
17 editions published between 2012 and 2014 in English and held by 68 WorldCat member libraries worldwide
One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. The purpose of this monograph is to present an elementary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use Dirichlet's energy as opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of Dirichlet's energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations, where normally only the second derivative or variation is calculated.¡ The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in either manifolds or complex analysis. Thus this monograph requires only the most basic knowledge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education
17 editions published between 2012 and 2014 in English and held by 68 WorldCat member libraries worldwide
One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. The purpose of this monograph is to present an elementary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use Dirichlet's energy as opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of Dirichlet's energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations, where normally only the second derivative or variation is calculated.¡ The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in either manifolds or complex analysis. Thus this monograph requires only the most basic knowledge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education
Architectuur in de natuur : de weg naar de optimale vorm by
Stefan Hildebrandt(
Book
)
1 edition published in 1989 in Dutch and held by 27 WorldCat member libraries worldwide
Studie over de ontwikkeling van de variatierekening
1 edition published in 1989 in Dutch and held by 27 WorldCat member libraries worldwide
Studie over de ontwikkeling van de variatierekening
Matemática y formas óptimas by
Stefan Hildebrandt(
Book
)
3 editions published in 1990 in Spanish and held by 22 WorldCat member libraries worldwide
3 editions published in 1990 in Spanish and held by 22 WorldCat member libraries worldwide
Lectures on integral equations by
Harold Widom(
Book
)
5 editions published between 1969 and 2016 in English and held by 15 WorldCat member libraries worldwide
5 editions published between 1969 and 2016 in English and held by 15 WorldCat member libraries worldwide
The Index Theorem for Minimal Surfaces of Higher Genus by
Friedrich Tomi(
Book
)
3 editions published in 1995 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 Hildebrandt, Stefan Author
 Marsden, Jerrold E. Author
 Dierkes, Ulrich Author
 Tomi, Friedrich Author
 McAloon, Kenneth Author
 Denzler, Jochen Other
 Weinstein, Alan 1943
 Widom, Harold Author
 Drasin, David
 Sauvigny, Friedrich
Useful Links
Associated Subjects
Boundary value problems Calculus Calculus of variations CalculusStudy and teaching Canada Critical point theory (Mathematical analysis) Differential equations, Nonlinear Differential equations, Partial Engineering Existence theorems Form (Philosophy) Functional analysis Functions of complex variables Geometry, Differential Geometry, Riemannian Global analysis (Mathematics) Global differential geometry Index theorems Integral equations Integrals Mathematics Mathematics in nature Minimal surfaces Motion Nature (Aesthetics) Plateau's problem Scientists Sequences (Mathematics) Teichmüller spaces United States Vector analysis
Alternative Names
Anthony Tromba American mathematician
Anthony Tromba Amerikaans wiskundige
Anthony Tromba USamerikanischer Mathematiker
Tromba, A. 1943
Tromba, A. J.
Tromba, A. J. 1943
Tromba, A. J. (Anthony Joseph)
Tromba, A. J. (Anthony Joseph), 1943
Tromba, Anthony.
Tromba, Anthony 1943
Tromba, Anthony J.
Tromba, Anthony J. 1943...
Tromba, Anthony J. (Anthony Joseph)
Tromba, Anthony J. (Anthony Joseph), 1943
Tromba, Anthony Joseph 1943
أنتوني ترومبا، 1943
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