https://en.wikipedia.org/wiki/Pompeiu_problem Pompeiu problem (抜粋) 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.
https://www.encyclopediaofmath.org/index.php/Pompeiu_problem Pompeiu problem. Carlos A. Berenstein (originator), Encyclopedia of Mathematics. This page was last modified on 7 February 2011,
