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

作者：Saroglou Christos^*

来源：Israel Journal of Mathematics, 2013, 195(2): 631-645.

DOI：10.1007/s11856-012-0111-3

Milman proved that there exists an absolute constant C %26gt; 0 such that, for every convex body K in a%26quot;e (n) , there exists a linear image TK of K with volume 1, such that |TK + D (n) |(1/n) a parts per thousand currency sign 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.

• 出版日期2013-6