Bibliographic Information

Lectures on convex geometry

Daniel Hug, Wolfgang Weil

(Graduate texts in mathematics, 286)

Springer, c2020

  • : [pbk]

Available at  / 2 libraries

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Note

"This Springer imprint is published by the registered company Springer Nature Switzerland AG ... Cham, Switzerland"--T.p. verso

Includes bibliographical references (p. 281-284) and index

Description and Table of Contents

Description

This book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn-Minkowski theory, with an exposition of mixed volumes, the Brunn-Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.

Table of Contents

Preface.- Preliminaries and Notation.- 1. Convex Sets.- 2. Convex Functions.- 3. Brunn-Minkowski Theory.- 4. From Area Measures to Valuations.- 5. Integral Geometric Formulas.-6. Solutions of Selected Exercises.- References.- Index.

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Details

  • NCID
    BC10859230
  • ISBN
    • 9783030501822
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    [Cham]
  • Pages/Volumes
    xviii, 287 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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