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The volume of the intersection of a convex body with its translates

Mathieu Meyer·Shlomo Reisner·M. Schmuckenschlager
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Abstract

It is proved that for a symmetric convex body K in R^n, if for some tau > 0, |K cap (x+tau K)| depends on ||x||_K only, then K is an ellipsoid. As a part of the proof, smoothness properties of convolution bodies ls are studied.

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Mathieu Meyer, Shlomo Reisner, M. Schmuckenschlager. 1992-04-14. The volume of the intersection of a convex body with its translates. https://arxiv.org/abs/math/9204212

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