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Pompeiu problem : ウィキペディア英語版 | Pompeiu problem In mathematics, the Pompeiu problem is a conjecture in integral geometry, named for Dimitrie Pompeiu, who posed the problem in 1929, as follows. Suppose ''f'' is a nonzero continuous function defined on a Euclidean space, and ''K'' is a simply connected Lipschitz domain, so that the integral of ''f'' vanishes on every congruent copy of ''K''. Then the domain is a ball. A special case is Schiffer's conjecture. ==References==
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