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Birkhäuser

Convexity and Its Applications

  • Book
  • © 1983

Overview

Editors:
  1. Peter M. Gruber

    1. Institut für Analysis, Technische Mathematik und Versicherungsmathematik, Technische Universität Wien, Wien, Austria

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  2. Jörg M. Wills

    1. Lehrstuhl für Mathematik II, Universität Siegen, Siegen 21, Germany

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Table of contents (16 chapters)

  1. Front Matter

    Pages 1-7
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  2. Convexity and Optimization in Discrete Structures July 1982

    • Achim Bachem
    Pages 9-29

  3. Isoperimetric inequalities

    • Catherine Bandle
    Pages 30-48

  4. Convex Bodies of Constant Width

    • G. D. Chakerian, H. Groemer
    Pages 49-96

  5. Algebraic Lattices

    • J. H. H. Chalk
    Pages 97-110

  6. The Twenty-Seven Lines on the Cubic Surface

    • H. S. M. Coxeter
    Pages 111-119

  7. Convexity Through the Ages

    • W. Fenchel
    Pages 120-130

  8. Approximation of convex bodies

    • Peter M. Gruber
    Pages 131-162

  9. Geometric convexity and differential geometry

    • Kurt Leichtweiss
    Pages 163-169

  10. Valuations on convex bodies

    • Peter McMullen, Rolf Schneider
    Pages 170-247

  11. Minimal and Closest Points Nonexpansive and Quasi-Nonexpansive Retractions in Real Banach Spaces

    • Pier Luigi Papini
    Pages 248-263

  12. Ellipsoids

    • Clinton M. Petty
    Pages 264-276

  13. Convexity in Banach spaces: some recent results

    • R. R. Phelps
    Pages 277-295

  14. Zonoids and Related Topics

    • Rolf Schneider, Wolfgang Weil
    Pages 296-317

  15. New Results in the Theory of Packing and Covering

    • G. Fejes Tóth
    Pages 318-359

  16. Stereology: A Survey for Geometers

    • Wolfgang Weil
    Pages 360-412

  17. Semi-Platonic Manifolds

    • J. M. Wills
    Pages 413-421
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Keywords

About this book

This collection of surveys consists in part of extensions of papers presented at the conferences on convexity at the Technische Universitat Wien (July 1981) and at the Universitat Siegen (July 1982) and in part of articles written at the invitation of the editors. This volume together with the earlier volume «Contributions to Geometry» edited by Tolke and Wills and published by Birkhauser in 1979 should give a fairly good account of many of the more important facets of convexity and its applications. Besides being an up to date reference work this volume can be used as an advanced treatise on convexity and related fields. We sincerely hope that it will inspire future research. Fenchel, in his paper, gives an historical account of convexity showing many important but not so well known facets. The articles of Papini and Phelps relate convexity to problems of functional analysis on nearest points, nonexpansive maps and the extremal structure of convex sets. A bridge to mathematical physics in the sense of Polya and Szego is provided by the survey of Bandle on isoperimetric inequalities, and Bachem's paper illustrates the importance of convexity for optimization. The contribution of Coxeter deals with a classical topic in geometry, the lines on the cubic surface whereas Leichtweiss shows the close connections between convexity and differential geometry. The exhaustive survey of Chalk on point lattices is related to algebraic number theory. A topic important for applications in biology, geology etc.

Editors and Affiliations

  • Institut für Analysis, Technische Mathematik und Versicherungsmathematik, Technische Universität Wien, Wien, Austria

    Peter M. Gruber

  • Lehrstuhl für Mathematik II, Universität Siegen, Siegen 21, Germany

    Jörg M. Wills

Bibliographic Information

  • Book Title: Convexity and Its Applications

  • Editors: Peter M. Gruber, Jörg M. Wills

  • DOI: https://doi.org/10.1007/978-3-0348-5858-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1983

  • Softcover ISBN: 978-3-0348-5860-1Published: 23 August 2014

  • eBook ISBN: 978-3-0348-5858-8Published: 11 November 2013

  • Edition Number: 1

  • Number of Pages: 421

  • Number of Illustrations: 19 b/w illustrations

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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