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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 | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

  • 1. S. R. Bell, The Cauchy Transform, Potential Theory, and Conformal Mapping. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1992. MR 1228442 (94k:30013)
  • 2. A. Sebbar and Th. Falliero, Equilibrium point of Green's function for the annulus and Eisenstein series. Proc. Amer. Math. Soc. 135 (2007), 313-328. MR 2255277 (2007h:30011)
  • 3. N. Suita, A. Yamada, On the Lu Qi-Keng conjecture. Proc. Amer. Math. Soc. 59 (1976), 222-224. MR 0425185 (54:13142)

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Additional Information

Alexander Yu. Solynin
Affiliation: Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409

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.

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