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Convexity and Its Applications

  • Peter M. Gruber
  • Jörg M. Wills

Table of contents

  1. Front Matter
    Pages 1-7
  2. Catherine Bandle
    Pages 30-48
  3. G. D. Chakerian, H. Groemer
    Pages 49-96
  4. J. H. H. Chalk
    Pages 97-110
  5. H. S. M. Coxeter
    Pages 111-119
  6. W. Fenchel
    Pages 120-130
  7. Peter M. Gruber
    Pages 131-162
  8. Kurt Leichtweiss
    Pages 163-169
  9. Peter McMullen, Rolf Schneider
    Pages 170-247
  10. Clinton M. Petty
    Pages 264-276
  11. Rolf Schneider, Wolfgang Weil
    Pages 296-317
  12. Wolfgang Weil
    Pages 360-412
  13. J. M. Wills
    Pages 413-421

About this book

Introduction

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.

Keywords

optimization research science and technology sets

Editors and affiliations

  • Peter M. Gruber
    • 1
  • Jörg M. Wills
    • 2
  1. 1.Institut für Analysis, Technische Mathematik und VersicherungsmathematikTechnische Universität WienWienAustria
  2. 2.Lehrstuhl für Mathematik IIUniversität SiegenSiegen 21Germany

Bibliographic information