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

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

1992-04-14

arxiv.org/abs/math/9204212v1

Mathematics

Functional Analysis

Scientific paper

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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