Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130 : Methods of Ordinary Differential Equations Applied to Elliptic Variational Problems. (AM-130) / Andrea Ratto, James Eells.

Format:

Book

Author/Creator:

Eells, James, author.

Ratto, Andrea, author.

Series:

Annals of mathematics studies ; no. 130.

Annals of Mathematics Studies ; 312

Language:

English

Subjects (All):

Harmonic maps.

Immersions (Mathematics).

Differential equations, Elliptic--Numerical solutions.

Differential equations, Elliptic.

Physical Description:

1 online resource (235 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Contents:

Frontmatter

INTRODUCTION

TABLE OF CONTENTS

PART 1. BASIC VARIATIONAL AND GEOMETRICAL PROPERTIES

PART 2. G-INVARIANT MINIMAL AND CONSTANT MEAN CURVATURE IMMERSIONS

PART 3. HARMONIC MAPS BETWEEN SPHERES

APPENDIX 1. SECOND VARIATIONS

APPENDIX 2. RIEMANNIAN IMMERSIONS Sm → Sn

APPENDIX 3. MINIMAL GRAPHS AND PENDENT DROPS

APPENDIX 4. FURTHER ASPECTS OF PENDULUM TYPE EQUATIONS

REFERENCES

INDEX

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400882502

1400882508

OCLC:

954123605