Some Nonlinear Problems in Riemannian Geometry

1. Front Matter

   Pages I-XVII

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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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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.

• Einstein Mannigfaltigkeiten
• Einstein manifolds
• Einstein-Kähler Matritzen
• Einstein-Kähler metrics
• Harmonische Maps
• Methoden zur Lösung nonlinearer Probleme
• Methods for nonlinear problems
• Riemannian geometry
• Yamabe Problem
• YellowSale2006
• curvature
• harmonic maps
• nicht-lineare p
• nicht-lineare partielle Differentialgleichungen
• nonlinear partial differential equations

• University of Paris VI, Mathematiques, Paris, France

  Thierry Aubin

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