Removable sets for intrinsic metric and for holomorphic functions

Sergei Kalmykov; Leonid V. Kovalev; Tapio Rajala

doi:10.1007/s11854-024-0076-2

Removable sets for intrinsic metric and for holomorphic functions

Sergei Kalmykov, Leonid V. Kovalev, Tapio Rajala

Department of Mathematics

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

6 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 language	English (US)
Pages (from-to)	751-772
Number of pages	22
Journal	Journal d'Analyse Mathematique
Volume	139
Issue number	2
DOIs	https://doi.org/10.1007/s11854-024-0076-2
State	Published - Oct 1 2019

ASJC Scopus subject areas

Analysis
General Mathematics

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Removable sets for intrinsic metric and for holomorphic functions

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