- Pompeiu problem
In
mathematics , the Pompeiu problem is a conjecture inintegral geometry , named forDimitrie Pompeiu , who posed the problem in 1929, as follows. Suppose "f" is a nonzerocontinuous function defined on a Euclidean space, and "K" is aLipschitz domain , so that theintegral of "f" vanishes on every congruent copy of "K". Then the domain is a ball.A special case is Schiffer's conjecture.
References
* 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.
External links
* [http://www.math.u-szeged.hu/~odor/pompeiu.htm]
* [http://eom.springer.de/P/p120150.htm]
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