Author: Frederick J. Almgren
Publisher: American Mathematical Soc.
ISBN: 0821827472
Category : Differential topology
Languages : en
Pages : 96
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Book Description
There have been many wonderful developments in the theory of minimal surfaces and geometric measure theory in the past 25 to 30 years. Many of the researchers who have produced these excellent results were inspired by this little book - or by Fred Almgren himself. The book is indeed a delightful invitation to the world of variational geometry. A central topic is Plateau's Problem, which is concerned with surfaces that model the behavior of soap films.When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This new tool makes possible much exciting new analysis and many new results. Plateau's problem and varifolds live in the world of geometric measure theory, where differential geometry and measure theory combine to solve problems which have variational aspects. The author's hope in writing this book was to encourage young mathematicians to study this fascinating subject further. Judging from the success of his students, it achieves this exceedingly well.
Author: Michael Struwe
Publisher:
ISBN: 9780691607757
Category : Calculus of variations
Languages : en
Pages : 0
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Book Description
Cover -- Contents -- A. The ""classical"" Plateau Problem for Disctype Minimal Surfaces. -- B. Surfaces of Prescribed Constant Mean Curvature
Author: Bob Sullivan
Publisher: Dutton Adult
ISBN: 9780525952800
Category : Business & Economics
Languages : en
Pages : 298
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Book Description
Demonstrates how athletes, artists and thinkers throughout the world are able to achieve high levels of potential, identifying principles for overcoming obstacles, enabling peak behaviors and avoiding time-wasting activities. Co-written by the author of Stop Getting Ripped Off.
Author: Themistocles M. Rassias
Publisher: World Scientific
ISBN: 9789810205560
Category : Mathematics
Languages : en
Pages : 350
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Book Description
This volume consists of papers written by eminent scientists from the international mathematical community, who present the latest information concerning the problem of Plateau after its classical solution by Jesse Douglas and Tibor Rad¢. The contributing papers provide insight and perspective on various problems in modern topics of Calculus of Variations, Global Differential Geometry and Global Nonlinear Analysis as related to the problem of Plateau.
Author: Maggie Paxson
Publisher: Penguin
ISBN: 1594634750
Category : Social Science
Languages : en
Pages : 370
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Book Description
Winner of the American Library in Paris Book Award Named a Best Book of 2019 by BookPage During World War II, French villagers offered safe harbor to countless strangers—mostly children—as they fled for their lives. The same place offers refuge to migrants today. Why? In a remote pocket of Nazi-held France, ordinary people risked their lives to rescue many hundreds of strangers, mostly Jewish children. Was this a fluke of history, or something more? Anthropologist Maggie Paxson, certainties shaken by years of studying strife, arrives on the Plateau to explore this phenomenon: What are the traits that make a group choose selflessness? In this beautiful, wind-blown place, Paxson discovers a tradition of offering refuge that dates back centuries. But it is the story of a distant relative that provides the beacon for which she has been searching. Restless and idealistic, Daniel Trocmé had found a life of meaning and purpose—or it found him—sheltering a group of children on the Plateau, until the Holocaust came for him, too. Paxson's journey into past and present turns up new answers, new questions, and a renewed faith in the possibilities for us all, in an age when global conflict has set millions adrift. Riveting, multilayered, and intensely personal, The Plateau is a deeply inspiring journey into the central conundrum of our time.
Author: Tibor Radó
Publisher: Springer
ISBN: 3642991181
Category : Mathematics
Languages : en
Pages : 114
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Book Description
The most immediate one-dimensional variation problem is certainly the problem of determining an arc of curve, bounded by two given and having a smallest possible length. The problem of deter points mining and investigating a surface with given boundary and with a smallest possible area might then be considered as the most immediate two-dimensional variation problem. The classical work, concerned with the latter problem, is summed up in a beautiful and enthusiastic manner in DARBOUX'S Theorie generale des surfaces, vol. I, and in the first volume of the collected papers of H. A. SCHWARZ. The purpose of the present report is to give a picture of the progress achieved in this problem during the period beginning with the Thesis of LEBESGUE (1902). Our problem has always been considered as the outstanding example for the application of Analysis and Geometry to each other, and the recent work in the problem will certainly strengthen this opinion. It seems, in particular, that this recent work will be a source of inspiration to the Analyst interested in Calculus of Variations and to the Geometer interested in the theory of the area and in the theory of the conformal maps of general surfaces. These aspects of the subject will be especially emphasized in this report. The report consists of six Chapters. The first three Chapters are important tools or concerned with investigations which yielded either important ideas for the proofs of the existence theorems reviewed in the last three Chapters.
Author: Hugh Thompson
Publisher: Penguin
ISBN: 0698183819
Category : Psychology
Languages : en
Pages : 321
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Book Description
Just try harder. Just work harder. Just do more. But what happens when working harder doesn’t seem to be getting you better results? You’ve got to get unstuck. In Getting Unstuck, Bob Sullivan and Hugh Thompson show the different kinds of plateaus that can hold you back and how they can be overcome. Using case studies of both success and failure—including Derek Jeter, Blockbuster, and Google—they identify how to avoid pitfalls and to incorporate the peak behaviors that place breakthroughs within anyone’s grasp. If you’ve ever given more and more to a broken relationship, a weight-loss regimen, or a stalled career—only to get less and less in return—Getting Unstuck will change your life.
Author: Gilles Deleuze
Publisher: A&C Black
ISBN: 9780826476944
Category : Philosophy
Languages : en
Pages : 716
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Book Description
‘A rare and remarkable book.' Times Literary Supplement Gilles Deleuze (1925-1995) was Professor of Philosophy at the University of Paris VIII. He is a key figure in poststructuralism, and one of the most influential philosophers of the twentieth century. Félix Guattari (1930-1992) was a psychoanalyst at the la Borde Clinic, as well as being a major social theorist and radical activist. A Thousand Plateaus is part of Deleuze and Guattari's landmark philosophical project, Capitalism and Schizophrenia - a project that still sets the terms of contemporary philosophical debate. A Thousand Plateaus provides a compelling analysis of social phenomena and offers fresh alternatives for thinking about philosophy and culture. Its radical perspective provides a toolbox for ‘nomadic thought' and has had a galvanizing influence on today's anti-capitalist movement. Translated by Brian Massumi>
Author: Xin Yuanlong
Publisher: World Scientific
ISBN: 9813236078
Category : Mathematics
Languages : en
Pages : 396
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Book Description
In the theory of minimal submanifolds, Bernstein's problem and Plateau's problem are central topics. This important book presents the Douglas-Rado solution to Plateau's problem, but the main emphasis is on Bernstein's problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and the author's own contributions to Bernstein type theorems for higher codimension. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds. This new edition contains the author's recent work on the Lawson-Osserman's problem for higher codimension, and on Chern's problem for minimal hypersurfaces in the sphere. Both Chern's problem and Lawson-Osserman's problem are important problems in minimal surface theory which are still unsolved. In addition, some new techniques were developed to address those problems in detail, which are of interest in the field of geometric analysis.
Author: T. Rado
Publisher: Springer Science & Business Media
ISBN: 3642652360
Category : Mathematics
Languages : en
Pages : 177
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Book Description
A convex function f may be called sublinear in the following sense; if a linear function l is ::=: j at the boundary points of an interval, then l:> j in the interior of that interval also. If we replace the terms interval and linear junction by the terms domain and harmonic function, we obtain a statement which expresses the characteristic property of subharmonic functions of two or more variables. This ge neralization, formulated and developed by F. RIEsz, immediately at tracted the attention of many mathematicians, both on account of its intrinsic interest and on account of the wide range of its applications. If f (z) is an analytic function of the complex variable z = x + i y. then If (z) I is subharmonic. The potential of a negative mass-distribu tion is subharmonic. In differential geometry, surfaces of negative curvature and minimal surfaces can be characterized in terms of sub harmonic functions. The idea of a subharmonic function leads to significant applications and interpretations in the fields just referred to, and· conversely, every one of these fields is an apparently in exhaustible source of new theorems on subharmonic functions, either by analogy or by direct implication.
