Handbook of Convex Geometry - Hardcover

Luisa, Bozzano G

Hardcover

ISBN 10: 0444895965 ISBN 13: 9780444895967

Publisher: North Holland, 1993

Synopsis

Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.

About this title

Synopsis

One aim of this handbook is to survey convex geometry, its many ramifications and its relations with other areas of mathematics. As such it should be a useful tool for the expert. A second aim is to give a high-level introduction to most branches of convexity and its applications, showing the major ideas, methods and results. This aspect should make it a source of inspiration for future researchers in convex geometry. The handbook should be useful for mathematicians working in other areas, as well as for econometrists, computer scientists, crystallographers, physicists and engineers who are looking for geometric tools for their own work. In particular, mathematicians specializing in optimization, functional analysis, number theory, probability theory, the calculus of variations and all branches of geometry should profit from this handbook.

Edition details

• Publisher: North Holland
• Publication date: 1993
• Language: English
• ISBN 10: 0444895965
• ISBN 13: 9780444895967
• Binding: Hardcover
• Number of pages: 801