Univalent Functions and the Pompeiu Problem

Nicola Garofalo, Fausto Segala
1994 Transactions of the American Mathematical Society  
In this paper we prove a result on the Pompeiu problem. If the Schwarz function 4> of the boundary of a simply-connected domain fi C R2 extends meromorphically into a certain portion E of ii with a pole at some point zn. 6 E , then ii has the Pompeiu property unless <1> is a Mobius transformation, in which case Q is a disk.
doi:10.2307/2154945 fatcat:7ctliereonas7du6voz44lwpw4