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Minimal surface area position of a convex body is not always an M-position

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Abstract

Milman proved that there exists an absolute constant C > 0 such that, for every convex body K in ℝn, there exists a linear image TK of K with volume 1, such that |TK + D n |1/n ≤ C, where D n is the Euclidean ball of volume 1. TK is then said to be in M-position. Giannopoulos and Milman asked if every convex body that has minimal surface area among all its affine images of volume 1 is also in M-position. We prove that the answer to this question is negative, even in the 1-unconditional case.

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  1. Department of Mathematics, University of Crete, 714-09, Heraklion, Crete, Greece

    Christos Saroglou

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  1. Christos Saroglou
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Correspondence to Christos Saroglou.

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Saroglou, C. Minimal surface area position of a convex body is not always an M-position. Isr. J. Math. 195, 631–645 (2013). https://doi.org/10.1007/s11856-012-0111-3

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  • DOI: https://doi.org/10.1007/s11856-012-0111-3

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