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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 ,
G. PAOURIS  and
CH. SAROGLOU
E. MARKESSINIS
Affiliation:
Department of Mathematics, University of Athens, Panepistimioupolis 157-84, Athens, Greece. e-mail: lefteris128@yahoo.gr
G. PAOURIS
Affiliation:
Department of Mathematics, Texas A & M University, College Station, TX 77843U.S.A. e-mail: grigoris@math.tamu.edu
CH. SAROGLOU
Affiliation:
Department of Mathematics, University of Crete, 714-09 Heraklion, Crete, Greece. e-mail: saroglou@math.uoc.gr
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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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 152 , Issue 1 , January 2012 , pp. 131 - 152
Copyright
Copyright © Cambridge Philosophical Society 2011

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