Title: Convex Analysis and Nonlinear Geometric Elliptic Equations
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.
Subjects: Global differential geometry, Mathematics, Global analysis (Mathematics), Mathematical physics, Differential equations, elliptic, Convex domains, Functions of real variables, Differential equations, partial, Differential Geometry, Analysis, Mathematical Methods in Physics, Numerical and Computational Physics