Removable sets for intrinsic metric and for holomorphic functions

Sergei Kalmykov, Leonid V. Kovalev, Tapio Rajala

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We study the subsets of metric spaces that are negligible for the infimal length of connecting curves; such sets are called metrically removable. In particular, we show that every closed totally disconnected set with finite Hausdorff measure of codimension 1 is metrically removable, which answers a question raised by Hakobyan and Herron. The metrically removable sets are shown to be related to other classes of “thin” sets that appeared in the literature. They are also related to the removability problems for classes of holomorphic functions with restrictions on the derivative.

Original languageEnglish (US)
Pages (from-to)751-772
Number of pages22
JournalJournal d'Analyse Mathematique
Volume139
Issue number2
DOIs
StatePublished - Oct 1 2019

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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