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AuthorAubin, Thierry. author
TitleSome Nonlinear Problems in Riemannian Geometry [electronic resource] / by Thierry Aubin
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998
Connect tohttp://dx.doi.org/10.1007/978-3-662-13006-3
Descript XVII, 398 p. online resource

SUMMARY

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

1 Riemannian Geometry -- 2 Sobolev Spaces -- 3 Background Material -- 4 Complementary Material -- 5 The Yamabe Problem -- 6 Prescribed Scalar Curvature -- 7 Einsteinโ{128}{148}Kรคhler Metrics -- 8 Mongeโ{128}{148}Ampรจre Equations -- 9 The Ricci Curvature -- 10 Harmonic Maps -- Bibliography* -- Notation


Mathematics Global analysis (Mathematics) Manifolds (Mathematics) Differential geometry Mathematics Differential Geometry Global Analysis and Analysis on Manifolds



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