Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590574 | Journal of Functional Analysis | 2014 | 43 Pages |
Abstract
Mahlerʼs conjecture asks whether the cube is a minimizer for the volume product of a body and its polar in the class of symmetric convex bodies in a fixed dimension. It is known that every Hanner polytope has the same volume product as the cube or the cross-polytope. In this paper we prove that every Hanner polytope is a strict local minimizer for the volume product in the class of symmetric convex bodies endowed with the Banach-Mazur distance.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jaegil Kim,