Some estimates for harmonic measures. III. (English) Zbl 0802.30017
[For parts I and II see Complex Analysis I, Lect. Notes Math. 1275, 210- 214 (1987; Zbl 0626.30023) and Proc. Am. Math. Soc. 111, No. 2, 441-442 (1991; Zbl 0728.30018).]
With a view to solve the problem of finding a continuum in the closed unit disc which meets every radius and whose harmonic measure at the centre is minimal, the author has already given a characterization of the class of continua in which such an extremal continuum must occur.
Here, the author gives a simplified derivation of this solution using the method of the extremal metric.
With a view to solve the problem of finding a continuum in the closed unit disc which meets every radius and whose harmonic measure at the centre is minimal, the author has already given a characterization of the class of continua in which such an extremal continuum must occur.
Here, the author gives a simplified derivation of this solution using the method of the extremal metric.
Reviewer: V.Anandam (Riyadh)
MSC:
| 30C85 | Capacity and harmonic measure in the complex plane |
| 31A15 | Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions |
References:
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| [3] | James A. Jenkins, On a problem concerning harmonic measure, Math. Z. 135 (1973/74), 279 – 283. · Zbl 0274.30019 · doi:10.1007/BF01215366 |
| [4] | 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. · doi:10.1007/BFb0078353 |
| [5] | Luby Liao, Certain extremal problems concerning module and harmonic measure, J. Analyse Math. 40 (1981), 1 – 42 (1982). · Zbl 0497.30019 · doi:10.1007/BF02790155 |
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