Stability of the Blaschke-Santaló and the affine isoperimetric inequality

Details Stability of the Blaschke-Santaló and the affine isoperimetric inequality Stability of the Blaschke-Santaló and the affine isoperimetric inequality

2009-01-21

arxiv.org/abs/0901.3340v1

Mathematics

Metric Geometry

Scientific paper

A stability version of the Blaschke-Santal\'o 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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