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Mathematics - Geometry & Topology | Some Nonlinear Problems in Riemannian Geometry

Some Nonlinear Problems in Riemannian Geometry

Aubin, Thierry

1998, XVII, 398 p.

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  • About this book

During the last few years, the field of nonlinear problems has undergone great development.This book, the core of which is the content of the author's earlier book (Springer-Verlag 1983), updated and extended in each chapter, and augmented by several completely new chapters, deals with some important geometric problems that have only recently been solved or partially been solved. Each problem is explained with the present status of its solution and the most recent methods of approaching the proofs. The main aim is to explain some methods and new techniques, and to apply them to problems coming from geometry or from physics. It deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, topological methods. ..........

Content Level » Research

Keywords » 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

Related subjects » Analysis - Geometry & Topology

Table of contents 

1 Riemannian Geometry.- 2 Sobolev Spaces.- 3 Background Material.- 4 Complementary Material.- 5 The Yamabe Problem.- 6 Prescribed Scalar Curvature.- 7 Einstein—Kähler Metrics.- 8 Monge—Ampère Equations.- 9 The Ricci Curvature.- 10 Harmonic Maps.- Bibliography*.- Notation.

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