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Comparing the M-position with some classical positions of convex bodies

Published online by Cambridge University Press:  21 October 2011

E. MARKESSINIS
Affiliation:
Department of Mathematics, University of Athens, Panepistimioupolis 157-84, Athens, Greece. e-mail: [email protected]
G. PAOURIS
Affiliation:
Department of Mathematics, Texas A & M University, College Station, TX 77843U.S.A. e-mail: [email protected]
CH. SAROGLOU
Affiliation:
Department of Mathematics, University of Crete, 714-09 Heraklion, Crete, Greece. e-mail: [email protected]

Abstract

The purpose of this paper is to compare some classical positions of convex bodies. We provide exact quantitative results which show that the minimal surface area position and the minimal mean width position are not necessarily M-positions. We also construct examples of unconditional convex bodies of minimal surface area that exhibit the worst possible behavior with respect to their mean width or their minimal hyperplane projection.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2011

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