This volume is intended to allow mathematicians and physicists, especially analysts, to learn about nonlinear problems which arise in Riemannian Geometry. Analysis on Riemannian manifolds is a field currently undergoing great development. More and more, analysis proves to be a very powerful means for solving geometrical problems. Conversely, geometry may help us to solve certain problems in analysis. There are several reasons why the topic is difficult and interesting. It is very large and almost unexplored. On the other hand, geometric problems often lead to limiting cases of known problems...

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...

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...