Continuity of logarithmic capacity

Sergei Kalmykov, Leonid V. Kovalev

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Article number125585
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Jan 1 2022


  • Green's function
  • Hausdorff metric
  • Logarithmic capacity
  • Uniformly perfect sets

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'Continuity of logarithmic capacity'. Together they form a unique fingerprint.

Cite this