Selected Topics in Convex Geometry

  • Maria Moszyńska

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Part I

  3. Part II

    1. Front Matter
      Pages 107-107
    2. Pages 159-171
  4. Part III

    1. Front Matter
      Pages 173-173
    2. Pages 175-183
    3. Pages 185-191

About this book

Introduction

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 Busemann–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.

Keywords

Convexity algebra ksa linear algebra measure measure theory optimization

Authors and affiliations

  • Maria Moszyńska
    • 1
  1. 1.Institute of MathematicsWarsaw UniversityWarsawPoland

Bibliographic information

  • DOI https://doi.org/10.1007/0-8176-4451-2
  • Copyright Information Birkhäuser Boston 2006
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4396-6
  • Online ISBN 978-0-8176-4451-2
  • About this book