02931nam a22005175i 4500978-3-662-13006-3DE-He21320151116133438.0cr nn 008mamaa130305s1998 gw : s :::: 0:eng d9783662130063978-3-662-13006-310.1007/978-3-662-13006-3doiENGDEQA641-670PBMPbicsscMAT012030bisacsh516.3623Online resource: SpringerAubin, Thierry.Some Nonlinear Problems in Riemannian Geometry[EBook] /by Thierry Aubin.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1998.XVII, 398 p.online resource.texttxtrdacontentcomputercrdamediaonline resourcecrrdacarriertext filePDFrdaSpringer Monographs in Mathematics,1439-73821 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.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. ..........Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)Mathematics.Global analysis (Mathematics).Manifolds (Mathematics).Differential geometry.Mathematics.Differential Geometry.Global Analysis and Analysis on Manifolds.SpringerLink (Online service)Springer eBooksPrinted edition:9783642082368Springer Monographs in Mathematics,1439-7382http://dx.doi.org/10.1007/978-3-662-13006-3ZDB-2-SMAZDB-2-BAEMathematics and Statistics (Springer-11649)