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Handbook of Convex Geometry (Hardcover)
Loot Price: R6,367
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Handbook of Convex Geometry (Hardcover)
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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.
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