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Licensed Unlicensed Requires Authentication Published by De Gruyter April 13, 2010

Visibility and diameter maximization of convex bodies

  • José Pedro Moreno EMAIL logo and Alberto Seeger
From the journal Forum Mathematicum

Abstract

This paper considers the problem of diameter maximization of a convex body in the Euclidean space and its connection with Valentine's notion of visibility. The so-called diametral spectrum, or set of critical lengths, is studied in depth from a topological point of view. As a side result, we give a new characterization of planar convex bodies of constant width. Our methodology emphasizes the role played by the concepts of critical pair and critical curve.

Received: 2008-10-20
Revised: 2009-04-01
Published Online: 2010-04-13
Published in Print: 2011-January

© de Gruyter 2011

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