Two Dimensional Geometric Variational Problems

Author : Jürgen Jost
Publisher : Unknown
Page : 256 pages
File Size : 42,8 Mb
Release : 1991-03-29
Category : Mathematics
ISBN : UOM:39015029249748

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Two-Dimensional Geometric Variational Problems by Jürgen Jost Pdf

This monograph treats variational problems for mappings from a surface equipped with a conformal structure into Euclidean space or a Riemannian manifold. Presents a general theory of such variational problems, proving existence and regularity theorems with particular conceptual emphasis on the geometric aspects of the theory and thorough investigation of the connections with complex analysis. Among the topics covered are: Plateau's problem, the regularity theory of solutions, a variational approach for obtaining various conformal representation theorems, a general existence theorem for harmonic mappings, and a new approach to Teichmuller theory via harmonic maps.

Author : Jürgen Jost
Publisher : Unknown
Page : 15 pages
File Size : 44,6 Mb
Release : 1987
Category : Electronic
ISBN : OCLC:632837529

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Twodimensional Geometric Variational Problems by Jürgen Jost Pdf

Author : Giuseppe Buttazzo,Mariano Giaquinta,Stefan Hildebrandt
Publisher : Oxford University Press
Page : 282 pages
File Size : 54,5 Mb
Release : 1998
Category : Mathematics
ISBN : 0198504659

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One-dimensional Variational Problems by Giuseppe Buttazzo,Mariano Giaquinta,Stefan Hildebrandt Pdf

While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory.

Author : A.T. Fomenko
Publisher : Routledge
Page : 290 pages
File Size : 42,8 Mb
Release : 2019-06-21
Category : Mathematics
ISBN : 9781351405676

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Variational Problems in Topology by A.T. Fomenko Pdf

Many of the modern variational problems of topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clear explanation of some of these problems (both solved and unsolved), using current methods of analytical topology. His book falls into three interrelated sections. The first gives an elementary introduction to some of the most important concepts of topology used in modern physics and mechanics: homology and cohomology, and fibration. The second investigates the significant role of Morse theory in modern aspects of the topology of smooth manifolds, particularly those of three and four dimensions. The third discusses minimal surfaces and harmonic mappings, and presents a number of classic physical experiments that lie at the foundations of modern understanding of multidimensional variational calculus. The author's skilful exposition of these topics and his own graphic illustrations give an unusual motivation to the theory expounded, and his work is recommended reading for specialists and non-specialists alike, involved in the fields of physics and mathematics at both undergraduate and graduate levels.

Author : Seiki Nishikawa,Richard Schoen
Publisher : Springer Science & Business Media
Page : 160 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9784431684022

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Lectures on Geometric Variational Problems by Seiki Nishikawa,Richard Schoen Pdf

In this volume are collected notes of lectures delivered at the First In ternational Research Institute of the Mathematical Society of Japan. This conference, held at Tohoku University in July 1993, was devoted to geometry and global analysis. Subsequent to the conference, in answer to popular de mand from the participants, it was decided to publish the notes of the survey lectures. Written by the lecturers themselves, all experts in their respective fields, these notes are here presented in a single volume. It is hoped that they will provide a vivid account of the current research, from the introduc tory level up to and including the most recent results, and will indicate the direction to be taken by future researeh. This compilation begins with Jean-Pierre Bourguignon's notes entitled "An Introduction to Geometric Variational Problems," illustrating the gen eral framework of the field with many examples and providing the reader with a broad view of the current research. Following this, Kenji Fukaya's notes on "Geometry of Gauge Fields" are concerned with gauge theory and its applications to low-dimensional topology, without delving too deeply into technical detail. Special emphasis is placed on explaining the ideas of infi nite dimensional geometry that, in the literature, are often hidden behind rigorous formulations or technical arguments.

Author : Francesco Maggi
Publisher : Cambridge University Press
Page : 475 pages
File Size : 48,6 Mb
Release : 2012-08-09
Category : Mathematics
ISBN : 9781139560894

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Sets of Finite Perimeter and Geometric Variational Problems by Francesco Maggi Pdf

The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. The theory of sets of finite perimeter provides a simple and effective framework. Topics covered include existence, regularity, analysis of singularities, characterization and symmetry results for minimizers in geometric variational problems, starting from the basics about Hausdorff measures in Euclidean spaces and ending with complete proofs of the regularity of area-minimizing hypersurfaces up to singular sets of codimension 8. Explanatory pictures, detailed proofs, exercises and remarks providing heuristic motivation and summarizing difficult arguments make this graduate-level textbook suitable for self-study and also a useful reference for researchers. Readers require only undergraduate analysis and basic measure theory.

Author : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 46,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783662223857

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Riemannian Geometry and Geometric Analysis by Jürgen Jost Pdf

FROM REVIEWS OF THE FIRST EDITION "a very readable introduction to Riemannian geometry...it is most welcome...The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references."-MATHEMATICAL REVIEWS

Author : Robert Osserman
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 50,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662034842

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Geometry V by Robert Osserman Pdf

Few people outside of mathematics are aware of the varieties of mathemat ical experience - the degree to which different mathematical subjects have different and distinctive flavors, often attractive to some mathematicians and repellant to others. The particular flavor of the subject of minimal surfaces seems to lie in a combination of the concreteness of the objects being studied, their origin and relation to the physical world, and the way they lie at the intersection of so many different parts of mathematics. In the past fifteen years a new component has been added: the availability of computer graphics to provide illustrations that are both mathematically instructive and esthetically pleas ing. During the course of the twentieth century, two major thrusts have played a seminal role in the evolution of minimal surface theory. The first is the work on the Plateau Problem, whose initial phase culminated in the solution for which Jesse Douglas was awarded one of the first two Fields Medals in 1936. (The other Fields Medal that year went to Lars V. Ahlfors for his contributions to complex analysis, including his important new insights in Nevanlinna Theory.) The second was the innovative approach to partial differential equations by Serge Bernstein, which led to the celebrated Bernstein's Theorem, stating that the only solution to the minimal surface equation over the whole plane is the trivial solution: a linear function.

Author : Richard M. Schoen
Publisher : Unknown
Page : 258 pages
File Size : 48,6 Mb
Release : 1977
Category : Calculus of variations
ISBN : STANFORD:36105031811313

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Existence and Regularity Theorems for Some Geometric Variational Problems by Richard M. Schoen Pdf

Author : Ulrich Dierkes,Stefan Hildebrandt,Anthony Tromba
Publisher : Springer Science & Business Media
Page : 547 pages
File Size : 54,9 Mb
Release : 2010-08-16
Category : Mathematics
ISBN : 9783642117060

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Global Analysis of Minimal Surfaces by Ulrich Dierkes,Stefan Hildebrandt,Anthony Tromba Pdf

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 Teichmüller 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.

Author : Hajime Urakawa
Publisher : World Scientific
Page : 349 pages
File Size : 44,7 Mb
Release : 2018-12-06
Category : Mathematics
ISBN : 9789813236417

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Geometry Of Biharmonic Mappings: Differential Geometry Of Variational Methods by Hajime Urakawa Pdf

'The present volume, written in a clear and precise style, ends with a rich bibliography of 167 items, including some classical books and papers. In the reviewer’s opinion, this excellent monograph will be a basic reference for graduate students and researchers working in the field of differential geometry of variational methods.'zbMATHThe author describes harmonic maps which are critical points of the energy functional, and biharmonic maps which are critical points of the bienergy functional. Also given are fundamental materials of the variational methods in differential geometry, and also fundamental materials of differential geometry.

Author : Demeter Krupka,David Saunders
Publisher : Elsevier
Page : 1243 pages
File Size : 46,6 Mb
Release : 2011-08-11
Category : Mathematics
ISBN : 9780080556734

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Handbook of Global Analysis by Demeter Krupka,David Saunders Pdf

This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents

Author : Ulrich Dierkes,Stefan Hildebrandt,Albrecht Küster,Ortwin Wohlrab
Publisher : Springer Science & Business Media
Page : 528 pages
File Size : 40,9 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9783662027912

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Minimal Surfaces I by Ulrich Dierkes,Stefan Hildebrandt,Albrecht Küster,Ortwin Wohlrab Pdf

Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can alsobe useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory fornonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.

Author : Paul Baird,Ahmad El Soufi,Ali Fardoun,Rachid Regbaoui
Publisher : Birkhäuser
Page : 158 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879682

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Variational Problems in Riemannian Geometry by Paul Baird,Ahmad El Soufi,Ali Fardoun,Rachid Regbaoui Pdf

This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. There are introductory survey articles as well as papers presenting the latest research results. Among the topics covered are blow-up theory for second order elliptic equations; bubbling phenomena in the harmonic map heat flow; applications of scans and fractional power integrands; heat flow for the p-energy functional; Ricci flow and evolution by curvature of networks of curves in the plane.

Author : Ulrich Dierkes,Stefan Hildebrandt,Albrecht Küster,Ortwin Wohlrab
Publisher : Springer Science & Business Media
Page : 435 pages
File Size : 44,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662087763

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Minimal Surfaces II by Ulrich Dierkes,Stefan Hildebrandt,Albrecht Küster,Ortwin Wohlrab Pdf

Minimal Surfaces I is an introduction to the field of minimal surfaces and a presentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can also be useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory for nonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.