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

• 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, 3, World Scientific, ISBN 981-281-105-2

External links

• 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,