[Banach] Abstract of a paper by Mathieu Meyer and Shlomo Reisner

This is an announcement for the paper "The isotropy constant and boundary properties of convex bodies" by Mathieu Meyer and Shlomo Reisner. Abstract: Let ${\cal K}^n$ be the set of all convex bodies in $\mathbb R^n$ endowed with the Hausdorff distance. We prove that if $K\in {\cal K}^n$ has positive generalized Gauss curvature at some point of its boundary, then $K$ is not a local maximizer for the isotropy constant $L_K$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 52A20, 53A05 Submitted from: reisner@math.haifa.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1512.02927 or http://arXiv.org/abs/1512.02927