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Bisections of Centrally Symmetric Planar Convex Bodies Minimizing the Maximum Relative Diameter

  • Antonio CañeteEmail author
  • Salvador Segura Gomis
Article
  • 30 Downloads

Abstract

In this paper, we study the bisections of a centrally symmetric planar convex body which minimize the maximum relative diameter functional. We give a necessary and a sufficient condition for a minimizing bisection, as well as analyze the behavior of the so-called standard bisection.

Keywords

Centrally symmetric planar convex bodies maximum relative diameter minimizing bisections 

Mathematics Subject Classification

Primary 52A40 Secondary 52A10 

Notes

Acknowledgements

The authors would like to thank the referees for useful comments which have improved these notes.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada IUniversidad de SevillaSevillaSpain
  2. 2.Departamento de Análisis MatemáticoUniversidad de AlicanteAlicanteSpain

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