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Two-Dimensional Geometric Variational Problems

Author: Jürgen Jost

Publisher:

Published: 1991-03-29

Total Pages: 256

ISBN-13:

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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.

Book Synopsis Two-Dimensional Geometric Variational Problems by : Jürgen Jost

Download or read book Two-Dimensional Geometric Variational Problems written by Jürgen Jost and published by . This book was released on 1991-03-29 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Twodimensional Geometric Variational Problems

Author: Jürgen Jost

Publisher:

Published: 1987

Total Pages: 15

ISBN-13:

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Book Synopsis Twodimensional Geometric Variational Problems by : Jürgen Jost

Download or read book Twodimensional Geometric Variational Problems written by Jürgen Jost and published by . This book was released on 1987 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:

One-dimensional Variational Problems

Author: Giuseppe Buttazzo

Publisher: Oxford University Press

Published: 1998

Total Pages: 282

ISBN-13: 9780198504658

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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.

Book Synopsis One-dimensional Variational Problems by : Giuseppe Buttazzo

Download or read book One-dimensional Variational Problems written by Giuseppe Buttazzo and published by Oxford University Press. This book was released on 1998 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Variational Problems in Topology

Author: A.T. Fomenko

Publisher: Routledge

Published: 2019-06-21

Total Pages: 290

ISBN-13: 1351405675

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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.

Book Synopsis Variational Problems in Topology by : A.T. Fomenko

Download or read book Variational Problems in Topology written by A.T. Fomenko and published by Routledge. This book was released on 2019-06-21 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Geometric Variational Problems

Author: Seiki Nishikawa

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 160

ISBN-13: 4431684026

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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.

Book Synopsis Lectures on Geometric Variational Problems by : Seiki Nishikawa

Download or read book Lectures on Geometric Variational Problems written by Seiki Nishikawa and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Sets of Finite Perimeter and Geometric Variational Problems

Author: Francesco Maggi

Publisher: Cambridge University Press

Published: 2012-08-09

Total Pages: 475

ISBN-13: 1139560891

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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.

Book Synopsis Sets of Finite Perimeter and Geometric Variational Problems by : Francesco Maggi

Download or read book Sets of Finite Perimeter and Geometric Variational Problems written by Francesco Maggi and published by Cambridge University Press. This book was released on 2012-08-09 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Riemannian Geometry and Geometric Analysis

Author: Jürgen Jost

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 460

ISBN-13: 3662223856

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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

Book Synopsis Riemannian Geometry and Geometric Analysis by : Jürgen Jost

Download or read book Riemannian Geometry and Geometric Analysis written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Existence and Regularity Theorems for Some Geometric Variational Problems

Author: Richard M. Schoen

Publisher:

Published: 1977

Total Pages: 258

ISBN-13:

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Book Synopsis Existence and Regularity Theorems for Some Geometric Variational Problems by : Richard M. Schoen

Download or read book Existence and Regularity Theorems for Some Geometric Variational Problems written by Richard M. Schoen and published by . This book was released on 1977 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometry V

Author: Robert Osserman

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 279

ISBN-13: 3662034840

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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.

Book Synopsis Geometry V by : Robert Osserman

Download or read book Geometry V written by Robert Osserman and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Variational Problems Related to Symplectic Geometry

Author: William P. Minicozzi (II.)

Publisher:

Published: 1994

Total Pages: 172

ISBN-13:

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Book Synopsis Geometric Variational Problems Related to Symplectic Geometry by : William P. Minicozzi (II.)

Download or read book Geometric Variational Problems Related to Symplectic Geometry written by William P. Minicozzi (II.) and published by . This book was released on 1994 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: