Convex Analysis and Nonlinear Geometric Elliptic Equations
By: by Ilya J. Bakelman
Publisher: Springer Berlin Heidelberg
Published: 1994
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 510
ISBN-13: 9783642698835; 9783642698811
Subjects: Global differential geometry; Mathematics; Global analysis (Mathematics); Mathematical physics
Description: This book is suitable as a graduate text and reference work in the areas of convex functions and bodies, global geometric problems, and nonlinear elliptic boundary value problems with special emphasis on Monge-Ampere equations. The theory of convex functions and bodies is presented first so that it can be used to study the other areas. In fact, the author makes a point of emphasizing the interrelationship of all the areas mentioned above. This enables the reader to obtain a working knowledge of the material. Specific topics of the book include the Minkowski problem, mixed volumes of convex bodies, the Brunn-Minkowski inequalities, geometric maximum principles, the normal mapping of convex hypersurfaces, the R-curvature of convex functions.
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