Selected Topics in Convex Geometry [Paperback]

Examines in detail those topics in convex geometry that are concerned with Euclidean space

Enriched by numerous examples, illustrations, and exercises, with a good bibliography and index

Requires only a basic knowledge of geometry, linear algebra, analysis, topology, and measure theory

Can be used for graduates courses or seminars in convex geometry, geometric and convex combinatorics, and convex analysis and optimization

* Preface to the Polish Edition * Preface to the English Edition * Introduction Part I: * Metric Spaces * Subsets of Euclidean Space * Basic Properties of Convex Sets * Transformations of the Space Kn of Compact Convex Sets * Rounding Theorems * Convex Polytopes * Functionals on the Space Kn...The Steiner Theorem * The Hadwiger Theorems * Applications of the Hadwiger Theorems Part II: * Curvature and Surface Area Measures * Sets with Positive Reach...Convexity Ring * Selectors for Convex Bodies * Polarity Part III: * Star Sets...Star Bodies * Intersection Bodies * Selectors for Star Bodies * Exercises to Part I * Exercises to Part II * Exercises to Part III * References * List of Symbols * Index

From the reviews:

This book is the translation and revision of the original Polish 2001 edition. Its focus is on studying convexity for its own sake rather than on applications of convexity & . The readable book contains numerous examples and some exercises. & the book could be used by students for courses or seminars in several geometric fields. (E. Hertel, Mathematical Reviews, Issue 2006 g)

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.