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.

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,

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