The Polya-Tchebotarov problem

Details The Polya-Tchebotarov problem The Polya-Tchebotarov problem

2008-09-15

arxiv.org/abs/0809.2483v1

Contemporary Mathematics AMS v. 505, 2010 pp 153-170

Mathematics

Complex Variables

Scientific paper

We describe the solutions to the problem of identifying the continuum in the complex plane that minimizes the logarithmic capacity among all the continuum that contain a prefixed finite set of points. This description can be implemented numerically and this can be used to improve the estimates on the Bloch-Landau constant and other related problems as the maximal expected lifetime of the Brownian motion on domains of inner radius one or the principal eigenvalue for the Laplace operator on such domains.

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