Extremal domains associated with an analytic function I
- 1 September 1985
- journal article
- research article
- Published by Taylor & Francis in Complex Variables and Elliptic Equations
- Vol. 4 (4) , 311-324
- https://doi.org/10.1080/17476938508814117
Abstract
In this paper we investigate the following two extremal problems: A) Let F be a continuum in the extended complex plane that does not divide and let f(z) be a function analytic on F By D we denote domains in such that f(z) has a single-valued analytic continuation in D. Does there exist a domain D 0 with minimal condenser capacity B) Let f(z) be a function analytic in a neighborhood of infinity. By D we denote domains in , such that f{z) has a single-valued analytic continuation in D. Does there exist a domain D 0 with minimal logarithmic capacity It is proved that there exist extremal domains D 0 in both problems. In a second part of the paper it will be shown that these domains are uniquely determined up to a boundary set of capacity zero.Keywords
This publication has 4 references indexed in Scilit:
- The structure of extremal domains associated with an analytic functionComplex Variables and Elliptic Equations, 1985
- Extremal domains associated with an analytic function IIComplex Variables and Elliptic Equations, 1985
- Extremal length, extremal regions and quadratic differentialsCommentarii Mathematici Helvetici, 1975
- Foundations of Modern Potential TheoryPublished by Springer Nature ,1972