Some estimates for harmonic measures. II
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- by James A. Jenkins PDF
- Proc. Amer. Math. Soc. 111 (1991), 441-442 Request permission
Abstract:
FitzGerald, Rodin, and Warschawski proved that, for a continuum of given diameter in the closed unit disc, the harmonic measure at the center is minimized when it is an arc on the circumference. A very simple proof of this result is given, using the method of the extremal metric.References
- Carl H. FitzGerald, Burton Rodin, and Stefan E. Warschawski, Estimates of the harmonic measure of a continuum in the unit disk, Trans. Amer. Math. Soc. 287 (1985), no. 2, 681–685. MR 768733, DOI 10.1090/S0002-9947-1985-0768733-1
- James A. Jenkins, Some estimates for harmonic measures, Complex analysis, I (College Park, Md., 1985–86) Lecture Notes in Math., vol. 1275, Springer, Berlin, 1987, pp. 210–214. MR 922301, DOI 10.1007/BFb0078353
- Akira Mori, On an absolute constant in the theory of quasi-conformal mappings, J. Math. Soc. Japan 8 (1956), 156–166. MR 79091, DOI 10.2969/jmsj/00820156
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 441-442
- MSC: Primary 30C85; Secondary 31A15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1050021-8
- MathSciNet review: 1050021