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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on equilibrium points of Green's function


Author: Alexander Yu. Solynin
Journal: Proc. Amer. Math. Soc. 136 (2008), 1019-1021
MSC (2000): Primary 30C40
Published electronically: November 1, 2007
MathSciNet review: 2361876
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Abstract: We answer a question raised by Ahmet Sebbar and Thérèse Falliero (2007) by showing that for every finitely connected planar domain $ \Omega$ there exists a compact subset $ K\subset \Omega$, independent of $ w$, containing all critical points of Green's function $ G(z,w)$ of $ \Omega$ with pole at $ w\in \Omega$.


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Additional Information

Alexander Yu. Solynin
Affiliation: Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409
Email: alex.solynin@ttu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09156-3
PII: S 0002-9939(07)09156-3
Keywords: Green's function, equilibrium point, Bergman function
Received by editor(s): December 18, 2006
Published electronically: November 1, 2007
Additional Notes: This research was supported in part by NSF grant DMS-0525339
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.