Removable sets for intrinsic metric and for holomorphic functions
Kalmykov, Sergei; Kovalev, Leonid V.; Rajala, Tapio (2019). Removable sets for intrinsic metric and for holomorphic functions. Journal d'Analyse Mathématique, 139 (2), 751-772. DOI: 10.1007/s11854-024-0076-2
Published inJournal d'Analyse Mathématique
© 2019 Springer
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.
PublisherSpringer; Hebrew University Magnes Press
Publication in research information system
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Related funder(s)Academy of Finland
Funding program(s)Research post as Academy Research Fellow, AoF
Additional information about fundingFirst author supported by NSFC grant 11650110426. Second author supported by the National Science Foundation grant DMS-1362453. Third author supported by the Academy of Finland project no. 274372.
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