Handbook of Convex Geometry, Volume B offers a survey of convex
geometry and its many ramifications and connections with other
fields of mathematics, including convexity, lattices,
crystallography, and convex functions. The selection first offers
information on the geometry of numbers, lattice points, and packing
and covering with convex sets. Discussions focus on packing in
non-Euclidean spaces, problems in the Euclidean plane, general
convex bodies, computational complexity of lattice point problem,
centrally symmetric convex bodies, reduction theory, and lattices
and the space of lattices. The text then examines finite packing
and covering and tilings, including plane tilings, monohedral
tilings, bin packing, and sausage problems. The manuscript takes a
look at valuations and dissections, geometric crystallography,
convexity and differential geometry, and convex functions. Topics
include differentiability, inequalities, uniqueness theorems for
convex hypersurfaces, mixed discriminants and mixed volumes,
differential geometric characterization of convexity, reduction of
quadratic forms, and finite groups of symmetry operations. The
selection is a dependable source of data for mathematicians and
researchers interested in convex geometry.
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