WorldCat Identities

Tromba, Anthony

Works: 140 works in 528 publications in 5 languages and 7,919 library holdings
Genres: Conference papers and proceedings  Examinations 
Roles: Author, Editor, htt
Classifications: QA303, 117
Publication Timeline
Most widely held works about Anthony Tromba
Most widely held works by Anthony Tromba
Vector calculus by Jerrold E Marsden( Book )

136 editions published between 1970 and 2018 in 4 languages and held by 1,755 WorldCat member libraries worldwide

This textbook by respected authors helps students foster computational skills and intuitive understanding with a careful balance of theory, applications, historical development and optional materials
Mathematics and optimal form by Stefan Hildebrandt( Book )

18 editions published between 1984 and 1985 in English and held by 1,170 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 )

13 editions published between 1995 and 1996 in English and held by 666 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
Regularity of minimal surfaces by Ulrich Dierkes( )

16 editions published between 2010 and 2013 in English and held by 474 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 H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet 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 that, for principal reasons, it is impossible to derive a priori estimates. Therefore regularity proofs for non-minimizers have to be based on indirect reasoning using monotonicity formulas. This is followed by a long chapter discussing geometric properties of minimal and H-surfaces such as enclosure theorems and isoperimetric inequalities, leading to the discussion of obstacle problems and of Plateau?þs problem for H-surfaces in a Riemannian manifold. A natural generalization of the isoperimetric problem is the so-called thread problem, dealing with minimal surfaces whose boundary consists of a fixed arc of given length. Existence and regularity of solutions are discussed. The final chapter on branch points presents a new approach to the theorem that area minimizing solutions of Plateau?þs problem have no interior branch points
A theory of branched minimal surfaces by Anthony Tromba( )

18 editions published between 2012 and 2014 in English and held by 473 WorldCat member libraries worldwide

1.Introduction -- 2.Higher order Derivatives of Dirichlets' Energy -- 3.Very Special Case; The Theorem for n + 1 Even and m + 1 Odd -- 4.The First Main Theorem; Non-Exceptional Branch Points -- 5.The Second Main Theorem: Exceptional Branch Points; The Condition k > l -- 6.Exceptional Branch Points Without The Condition k > l -- 7.New Brief Proofs of the Gulliver-Osserman-Royden Theorem -- 8.Boundary Branch Points -- Scholia -- Appendix -- Bibliography.​
Global analysis of minimal surfaces by Ulrich Dierkes( )

19 editions published between 2010 and 2013 in English and held by 379 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 'edge-crawling' 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
Teichmüller theory in Riemannian geometry by Anthony Tromba( Book )

21 editions published in 1992 in 3 languages and held by 373 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 1980-1986. 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 achdiplom-Vorlesungen 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 quasi-conformal mappings (in this approach we completely avoid the use of quasi-conformal 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
Existence theorems for minimal surfaces of non-zero genus spanning a contour by Friedrich Tomi( Book )

11 editions published in 1988 in English and held by 279 WorldCat member libraries worldwide

We present a modern approach to the classical problem of Plateau based purely on differential geometric concepts. We not only reprove the classical results of Douglas but also develop a new geometric criterion on a given finite system of disjoint Jordan curves in three-dimensional Euclidean space which guarantees the existence of a minimal surface of a prescribed genus having these curves as boundary
The index theorem for minimal surfaces of higher genus by Friedrich Tomi( Book )

13 editions published in 1995 in English and held by 275 WorldCat member libraries worldwide

In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces
On the number of simply connected minimal surfaces spanning a curve by Anthony Tromba( Book )

11 editions published in 1977 in English and held by 255 WorldCat member libraries worldwide

The classical problem of Plateau is studied from the point of view of global nonlinear analysis. It is shown that minimal surfaces of the topological type of the two disc arise as the zeros of a Fredholm vector field on an infinite dimensional manifold. A framework is developed to prove the finiteness of solutions for an open and dense set of curves and to count the number of such solutions according to sign, although the complete results in this direction are not proved in this paper
Seminar on New Results in Nonlinear Partial Differential Equations : a publication of the Max-Planck-Institut für Mathematik, Bonn by Anthony Tromba( Book )

18 editions published between 1987 and 2012 in English and German and held by 234 WorldCat member libraries worldwide

Recent years have seen a tremendous growth of interest in non-linear partial differential equations_ Yau's solution of the Calabi conjecture and more recently Schoen's solution of the Yamabe problem and Wente's counter-example 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., January-September 1984 at the Max-Planck-I 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 non-linear 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 counter-examples to Hopf's conjecture, and, due to Uwe Abresch, a further development of these ideas. Sergiu Klainerman's global existence result for the non-linear Klein-Gordon equation in four space-time dimensions, achieved while at Max Planck, is included. Vince Moncrief presents his global existence result for the Yang-Mills equation in Min kowski space time. All of these results answer important and outstanding questions
Calculus by Kenneth McAloon( Book )

4 editions published in 1972 in English and held by 230 WorldCat member libraries worldwide

Introductory course for students with a high-school background of algebra, geometry and rudiments of trigonometry
Basic multivariable calculus by Jerrold E Marsden( Book )

22 editions published between 1993 and 2000 in 3 languages and held by 219 WorldCat member libraries worldwide

Mathématiques et formes optimales : l'explication des structures naturelles by Stefan Hildebrandt( Book )

7 editions published between 1986 and 1998 in French and English and held by 138 WorldCat member libraries worldwide

Calculus of one variable by Kenneth McAloon( Book )

5 editions published in 1972 in English and held by 122 WorldCat member libraries worldwide

Panoptimum : mathematische Grundmuster des Vollkommenen by Stefan Hildebrandt( Book )

3 editions published in 1987 in German and held by 114 WorldCat member libraries worldwide

Seifenblasen und andere Minimalflächen - genau besehen von 2 Mathematikern
Kugel, Kreis und Seifenblasen : optimale Formen in Geometrie und Natur by Stefan Hildebrandt( Book )

5 editions published in 1996 in German and held by 104 WorldCat member libraries worldwide

Vektoranalysis : Einführung, Aufgaben, Lösungen by Jerrold E Marsden( Book )

4 editions published in 1995 in German and held by 102 WorldCat member libraries worldwide

Lectures on integral equations by Harold Widom( )

7 editions published between 1969 and 2016 in English and held by 65 WorldCat member libraries worldwide

This concise and classic volume presents the main results of integral equation theory as consequences of the theory of operators on Banach and Hilbert spaces. In addition, it offers a brief account of Fredholm's original approach. The self-contained treatment requires only some familiarity with elementary real variable theory, including the elements of Lebesgue integration, and is suitable for advanced undergraduates and graduate students of mathematics. Other material discusses applications to second order linear differential equations, and a final chapter uses Fourier integral techniques to investigate certain singular integral equations of interest for physical applications as well as for their own sake. A helpful index concludes the text
Minimal surfaces by Ulrich Dierkes( Book )

2 editions published in 2010 in English and held by 57 WorldCat member libraries worldwide

Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341). 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 three-dimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently, as surfaces of zero mean curvature. The final definition of a minimal surface is that of a nonconstant harmonic mapping X: \Omega\to\R^3 which is conformally parametrized on \Omega\subset\R^2 and may have branch points. Thereafter the classical theory of minimal surfaces is surveyed, comprising many examples, a treatment of Bj?œrling?þs initial value problem, reflection principles, a formula of the second variation of area, the theorems of Bernstein, Heinz, Osserman, and Fujimoto. The second part of this volume begins with a survey of Plateau?þs problem and of some of its modifications. One of the main features is a new, completely elementary proof of the fact that area A and Dirichlet integral D have the same infimum in the class C(G) of admissible surfaces spanning a prescribed contour G. This leads to a new, simplified solution of the simultaneous problem of minimizing A and D in C(G), as well as to new proofs of the mapping theorems of Riemann and Korn-Lichtenstein, and to a new solution of the simultaneous Douglas problem for A and D where G consists of several closed components. Then basic facts of stable minimal surfaces are derived; this is done in the context of stable H-surfaces (i.e. of stable surfaces of prescribed mean curvature H), especially of cmc-surfaces (H = const), and leads to curvature estimates for stable, immersed cmc-surfaces and to Nitsche?þs uniqueness theorem and Tomi?þs finiteness result. In addition, a theory of unstable solutions of Plateau?þs problems is developed which is based on Courant?þs mountain pass lemma. Furthermore, Dirichlet?þs problem for nonparametric H-surfaces is solved, using the solution of Plateau?þs problem for H-surfaces and the pertinent estimates
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The parsimonious universe : shape and form in the natural world
The parsimonious universe : shape and form in the natural worldRegularity of minimal surfacesGlobal analysis of minimal surfacesTeichmüller theory in Riemannian geometryThe index theorem for minimal surfaces of higher genusBasic multivariable calculusMinimal surfaces
Alternative Names
Anthony Joseph Tromba

Anthony Tromba American mathematician

Anthony Tromba Amerikaans wiskundige

Anthony Tromba matemàtic estatunidenc

Anthony Tromba matemático estadounidense

Anthony Tromba mathématicien américain

Anthony Tromba US-amerikanischer 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

Tromba, Anthony Joseph 1943-

أنتوني ترومبا، 1943-

English (274)

Spanish (50)

German (14)

French (6)

Esperanto (3)