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A note on equilibrium points of Green's function

Author(s): Alexander Yu. Solynin
Journal: Proc. Amer. Math. Soc. 136 (2008), 1019-1021.
MSC (2000): Primary 30C40
Posted: November 1, 2007
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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 , containing all critical points of Green's function of $\Omega$ with pole at $w\in \Omega$ .

References:

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
Email: alex.solynin@ttu.edu

DOI: 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
Posted: November 1, 2007
Additional Notes: This research was supported in part by NSF grant DMS-0525339
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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