The field of convex geometry has become a fertile subject of
mathematical activity in the past few decades. This exposition,
examining in detail those topics in convex geometry that are
concerned with Euclidean space, is enriched by numerous examples,
illustrations, and exercises, with a good bibliography and index.
The theory of intrinsic volumes for convex bodies, along with
the Hadwiger characterization theorems, whose proofs are based on
beautiful geometric ideas such as the rounding theorems and the
Steiner formula, are treated in Part 1. In Part 2 the reader is
given a survey on curvature and surface area measures and
extensions of the class of convex bodies. Part 3 is devoted to the
important class of star bodies and selectors for convex and star
bodies, including a presentation of two famous problems of
geometric tomography: the Shephard problem and the Busemanna "Petty
problem.
Selected Topics in Convex Geometry requires of the reader only a
basic knowledge of geometry, linear algebra, analysis, topology,
and measure theory. The book can be used in the classroom setting
for graduates courses or seminars in convex geometry, geometric and
convex combinatorics, and convex analysis and optimization.
Researchers in pure and applied areas will also benefit from the
book.
General
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