The volume of the intersection of a convex body with its translates
Mathieu Meyer, Shlomo Reisner, M. Schmuckenschlager
Abstract
It is proved that for a symmetric convex body K in Rn, 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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