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Some estimates for harmonic measures. II


Author: James A. Jenkins
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
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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 [Enhancements On Off] (What's this?)

  • [1] C. FitzGerald, B. Rodin, and S. Warschawski, Estimates of the harmonic measure of a continuum in the unit disc, Trans. Amer. Math. Soc. 287 (1985), 681-685. MR 768733 (86e:30021)
  • [2] James A. Jenkins, Some estimates for harmonic measures, in Complex Analysis I (Proc. of the Special Year, University of Maryland, College Park, 1985-86), Lecture Notes in Math., vol. 1275, Springer-Verlag, 1987, pp. 210-214. MR 922301 (89d:30028)
  • [3] A. Mori, On an absolute constant in the theory of quasiconformal mappings, J. Math. Soc. Japan 8 (1956), 156-166. MR 0079091 (18:27e)

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DOI: https://doi.org/10.1090/S0002-9939-1991-1050021-8
Article copyright: © Copyright 1991 American Mathematical Society

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