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arXiv · 0901.3340

Stability of the Blaschke-Santaló and the affine isoperimetric inequality

Károly J. Böröczky
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Abstract

A stability version of the Blaschke-Santaló inequality and the affine isoperimetric inequality for convex bodies of dimension n>2 is proved. The first step is the reduction to the case when the convex body is o-symmetric and has axial rotational symmetry. This step works for related inequalities compatible with Steiner symmetrization. Secondly, for these convex bodies, a stability version of the characterization of ellipsoids by the fact that each hyperplane section is centrally symmetric is established.

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Károly J. Böröczky. 2009-01-21. Stability of the Blaschke-Santaló and the affine isoperimetric inequality. https://arxiv.org/abs/0901.3340

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