High Quality Content by WIKIPEDIA articles! 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 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.

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