Pompeiu problem

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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 Lipschitz domain K in Euclidean space, 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.

[edit] Reference

  • Dimitrie Pompeiu, Sur certains systèmes d'équations linéaires et sur une propriété intégrale des fonctions de plusieurs variables, Comptes Rendus de l'Académie des Sciences Paris Série I. Mathématique, 188 (1929), 1138 –1139.

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