Nonlinear Analysis on Manifolds. Monge-Ampère Equations

  • Thierry Aubin

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 252)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Thierry Aubin
    Pages 1-31
  3. Thierry Aubin
    Pages 32-69
  4. Thierry Aubin
    Pages 70-100
  5. Thierry Aubin
    Pages 101-114
  6. Thierry Aubin
    Pages 115-124
  7. Thierry Aubin
    Pages 125-138
  8. Thierry Aubin
    Pages 157-188
  9. Back Matter
    Pages 189-204

About this book

Introduction

This volume is intended to allow mathematicians and physicists, especially analysts, to learn about nonlinear problems which arise in Riemannian Geometry. Analysis on Riemannian manifolds is a field currently undergoing great development. More and more, analysis proves to be a very powerful means for solving geometrical problems. Conversely, geometry may help us to solve certain problems in analysis. There are several reasons why the topic is difficult and interesting. It is very large and almost unexplored. On the other hand, geometric problems often lead to limiting cases of known problems in analysis, sometimes there is even more than one approach, and the already existing theoretical studies are inadequate to solve them. Each problem has its own particular difficulties. Nevertheless there exist some standard methods which are useful and which we must know to apply them. One should not forget that our problems are motivated by geometry, and that a geometrical argument may simplify the problem under investigation. Examples of this kind are still too rare. This work is neither a systematic study of a mathematical field nor the presentation of a lot of theoretical knowledge. On the contrary, I do my best to limit the text to the essential knowledge. I define as few concepts as possible and give only basic theorems which are useful for our topic. But I hope that the reader will find this sufficient to solve other geometrical problems by analysis.

Keywords

Eigenvalue Interpolation Jacobi field Riemannian geometry Riemannian manifold Tensor curvature differential geometry manifold

Authors and affiliations

  • Thierry Aubin
    • 1
  1. 1.Universite de Paris VI MathematiquesParis, Cedex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5734-9
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-5736-3
  • Online ISBN 978-1-4612-5734-9
  • Series Print ISSN 0072-7830
  • About this book
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