Handbook of Convex Geometry

Handbook of Convex Geometry

by Bozzano G Luisa
ISBN-10:
0444895965
ISBN-13:
9780444895967
Pub. Date:
08/24/1993
Publisher:
Elsevier Science
ISBN-10:
0444895965
ISBN-13:
9780444895967
Pub. Date:
08/24/1993
Publisher:
Elsevier Science
Handbook of Convex Geometry

Handbook of Convex Geometry

by Bozzano G Luisa
$305.0 Current price is , Original price is $305.0. You
$305.00 
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Overview

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.

Product Details

ISBN-13: 9780444895967
Publisher: Elsevier Science
Publication date: 08/24/1993
Series: Handbooks of Geometry
Pages: 801
Product dimensions: 1.69(w) x 7.00(h) x 10.00(d)

Table of Contents

VOLUME B. Preface. Part 3: Discrete Aspects of Convexity. Geometry of Numbers (P.M. Gruber). Lattice points (P. Gritzmann, J.M. Wills). Packing and covering with convex sets (G. Fejes Tóth, W. Kuperberg). Finite packing and covering (P. Gritzmann, J.M. Wills). Tilings (E. Schulte). Valuations and dissections (P. McMullen). Geometric crystallography (P. Engel). Part 4: Analytic Aspects of Convexity. Convexity and differential geometry (K. Leichtweiss). Convex functions (A.W. Roberts). Convexity and calculus of variations (U. Brechtken-Manderscheid, E. Heil). On isoperimetric theorems of mathematical physics (G. Talenti). The local theory of normed spaces and its applications to convexity (J. Lindenstrauss, V. Milman). Nonexpansive maps and fixed points (P.L. Papini). Critical Exponents (V. Pták). Fourier series and spherical harmonics in convexity (H. Groemer). Zonoids and generalisations (P. Goodey, W. Weil). Baire categories in convexity (P.M. Gruber). Part 5: Stochastic Aspects of Convexity. Integral geometry (R. Schneider, J.A. Wieacker). Stochastic geometry (W. Weil, J.A. Wieacker). Author Index. Subject Index.
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