Continuity of logarithmic capacity

Sergei Kalmykov; Leonid V. Kovalev

doi:10.1016/j.jmaa.2021.125585

Continuity of logarithmic capacity

Sergei Kalmykov, Leonid V. Kovalev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the continuity of logarithmic capacity under Hausdorff convergence of uniformly perfect planar sets. The continuity holds when the Hausdorff distance to the limit set tends to zero at sufficiently rapid rate, compared to the decay of the parameters involved in the uniformly perfect condition. The continuity may fail otherwise.

Original language	English (US)
Article number	125585
Journal	Journal of Mathematical Analysis and Applications
Volume	505
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2021.125585
State	Published - Jan 1 2022

Keywords

Green's function
Hausdorff metric
Logarithmic capacity
Uniformly perfect sets

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2021.125585

Cite this

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title = "Continuity of logarithmic capacity",

abstract = "We prove the continuity of logarithmic capacity under Hausdorff convergence of uniformly perfect planar sets. The continuity holds when the Hausdorff distance to the limit set tends to zero at sufficiently rapid rate, compared to the decay of the parameters involved in the uniformly perfect condition. The continuity may fail otherwise.",

keywords = "Green's function, Hausdorff metric, Logarithmic capacity, Uniformly perfect sets",

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Continuity of logarithmic capacity

Abstract

Keywords

ASJC Scopus subject areas

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