Leírás
A well-known conjecture asserts that the isotropic constant is maximized among /n/-dimensional convex bodies by the simplex. Supporting evidence for this conjecture is provided by a result due to Rademacher: a simplicial polytope /P/ that is locally maximizing has to be a simplex. In this talk, we discuss necessary conditions for a polytope /P/ to be a local maximizer of the isotropic constant and present several strengthenings and variations of Rademacher's result. In particular, we show that the existence of a simplicial vertex is sufficient to conclude that /P/ is a simplex. In the centrally symmetric setting, the assumption that /P/ has a simplicial vertex implies that /P/ is a cross-polytope, and the assumption that /P/ is a zonotope with a cubical zone implies that /P/ is a cube.
The talk will also be broadcast on Zoom.