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Nonlinear Analysis on Manifolds. Monge-Ampere Equations (Hardcover, 1982 ed.)
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Nonlinear Analysis on Manifolds. Monge-Ampere Equations (Hardcover, 1982 ed.)
Series: Grundlehren der mathematischen Wissenschaften, 252
Expected to ship within 10 - 15 working days
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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.
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