Nonlinear Analysis on Manifolds. Monge-Ampère Equations

Nonlinear Analysis on Manifolds. Monge-Ampère Equations (Grundlehren der mathematischen Wissenschaften, 252)

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 in analysis, sometimes there is even more than one approach, and the already existing theoretical studies are inadequate to solve them. Each problem has its own particular difficulties. Nevertheless there exist some standard methods which are useful and which we must know to apply them. One should not forget that our problems are motivated by geometry, and that a geometrical argument may simplify the problem under investigation. Examples of this kind are still too rare. This work is neither a systematic study of a mathematical field nor the presentation of a lot of theoretical knowledge. On the contrary, I do my best to limit the text to the essential knowledge. I define as few concepts as possible and give only basic theorems which are useful for our topic. But I hope that the reader will find this sufficient to solve other geometrical problems by analysis.
Country USA
Brand Springer
Manufacturer Springer
Binding Hardcover
ReleaseDate 1982-12-15
UnitCount 1
EANs 9780387907048

Country	USA
Brand	Springer
Manufacturer	Springer
Binding	Hardcover
ReleaseDate	1982-12-15
UnitCount	1
EANs	9780387907048

Nonlinear Analysis on Manifolds. Monge-Ampère Equations (Grundlehren der mathematischen Wissenschaften, 252)

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