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Some Nonlinear Problems in Riemannian Geometry

  • Book
  • © 1998

Overview

Authors:
  1. Thierry Aubin

    1. University of Paris VI, Mathematiques, Paris, France

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Part of the book series: Springer Monographs in Mathematics (SMM)

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About this book

During the last few years, the field of nonlinear problems has undergone great development. This book consisting of the updated Grundlehren volume 252 by the author and of a newly written part, deals with some important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved. Each problem is explained, up-to-date results are given and proofs are presented. Thus, the reader is given access, for each specific problem, to its present status of solution as well as to the most up-to-date methods for approaching it. The main objective of the book is to explain some methods and new techniques, and to apply them. It deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber.

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XVII
    Download chapter PDF

  2. Riemannian Geometry

    • Thierry Aubin
    Pages 1-31

  3. Sobolev Spaces

    • Thierry Aubin
    Pages 32-69

  4. Background Material

    • Thierry Aubin
    Pages 70-100

  5. Complementary Material

    • Thierry Aubin
    Pages 101-144

  6. The Yamabe Problem

    • Thierry Aubin
    Pages 145-193

  7. Prescribed Scalar Curvature

    • Thierry Aubin
    Pages 194-250

  8. Einstein-Kähler Metrics

    • Thierry Aubin
    Pages 251-288

  9. Monge-Ampère Equations

    • Thierry Aubin
    Pages 289-320

  10. The Ricci Curvature

    • Thierry Aubin
    Pages 321-347

  11. Harmonic Maps

    • Thierry Aubin
    Pages 348-364

  12. Back Matter

    Pages 365-397
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Authors and Affiliations

  • University of Paris VI, Mathematiques, Paris, France

    Thierry Aubin

Bibliographic Information

  • Book Title: Some Nonlinear Problems in Riemannian Geometry

  • Authors: Thierry Aubin

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-13006-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Hardcover ISBN: 978-3-540-60752-6Published: 22 June 1998

  • Softcover ISBN: 978-3-642-08236-8Published: 06 December 2010

  • eBook ISBN: 978-3-662-13006-3Published: 09 March 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XVII, 397

  • Topics: Differential Geometry, Global Analysis and Analysis on Manifolds

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