The isotropy constant and boundary properties of convex bodies

Meyer, Mathieu; Reisner, Shlomo

doi:10.1090/proc/13143

The isotropy constant and boundary properties of convex bodies
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Proc. Amer. Math. Soc. 144 (2016), 3935-3947 Request permission

Abstract:

Let $\mathcal {K}^n$ be the set of all convex bodies in $\mathbb {R}^n$ endowed with the Hausdorff distance. We prove that if $K\in \mathcal {K}^n$ has positive generalized Gauss curvature at some point of its boundary, then $K$ is not a local maximizer for the isotropy constant $L_K$.

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