Univalent functions and the Pompeiu problem

Authors:
Nicola Garofalo and Fausto Segàla

Journal:
Trans. Amer. Math. Soc. **346** (1994), 137-146

MSC:
Primary 30E15; Secondary 35N05

DOI:
https://doi.org/10.1090/S0002-9947-1994-1250819-4

MathSciNet review:
1250819

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Abstract: In this paper we prove a result on the Pompeiu problem. If the Schwarz function of the boundary of a simply-connected domain extends meromorphically into a certain portion of with a pole at some point , then has the Pompeiu property unless is a Möbius transformation, in which case is a disk.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1250819-4

Article copyright:
© Copyright 1994
American Mathematical Society