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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 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.
- Pompeiu, Dimitrie (1929), "Sur certains systèmes d'équations linéaires et sur une propriété intégrale des fonctions de plusieurs variables", Comptes Rendus de l'Académie des Sciences, Série I, 188: 1138–1139
- Ciatti, Paolo (2008), Topics in mathematical analysis, Series on analysis, applications and computation, vol. 3, World Scientific, ISBN 978-981-281-105-9
- Pompeiu problem at Department of Geometry, Bolyai Institute, University of Szeged, Hungary
- Pompeiu problem at SpringerLink encyclopaedia of mathematics
- The Pompeiu problem,
- Schiffer's conjecture,
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