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Removable sets for intrinsic metric and for holomorphic functions

  • Sergei Kalmykov
  • Leonid V. KovalevEmail author
  • Tapio Rajala
Article

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.

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Notes

Acknowledgment

We thank the referee for carefully reading themanuscript and suggesting several improvements.

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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  • Sergei Kalmykov
    • 1
  • Leonid V. Kovalev
    • 2
    Email author
  • Tapio Rajala
    • 3
  1. 1.School of mathematical sciencesShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Mathematics DepartmentSyracuse UniversitySyracuseUSA
  3. 3.Department of Mathematics and StatisticsUniversity of JyvaskylaJyvaskylaFinland

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