A note on equilibrium points of Green’s function
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- by Alexander Yu. Solynin PDF
- Proc. Amer. Math. Soc. 136 (2008), 1019-1021 Request permission
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
- Steven R. Bell, The Cauchy transform, potential theory, and conformal mapping, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. MR 1228442
- Ahmed Sebbar and Thérèse Falliero, Equilibrium point of Green’s function for the annulus and Eisenstein series, Proc. Amer. Math. Soc. 135 (2007), no. 2, 313–328. MR 2255277, DOI 10.1090/S0002-9939-06-08353-5
- Nobuyuki Suita and Akira Yamada, On the Lu Qi-keng conjecture, Proc. Amer. Math. Soc. 59 (1976), no. 2, 222–224. MR 425185, DOI 10.1090/S0002-9939-1976-0425185-9
Additional Information
- Alexander Yu. Solynin
- Affiliation: Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409
- MR Author ID: 206458
- Email: alex.solynin@ttu.edu
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1019-1021
- MSC (2000): Primary 30C40
- DOI: https://doi.org/10.1090/S0002-9939-07-09156-3
- MathSciNet review: 2361876