How to recognize convexity of a set from its marginals
classification
🧮 math.MG
math.FA
keywords
marginalsfiniteontoperimeterconvexconvexityhyperplanehyperplanes
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We investigate the regularity of the marginals onto hyperplanes for sets of finite perimeter. We prove, in particular, that if a set of finite perimeter has log-concave marginals onto a.e. hyperplane then the set is convex.
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