@article{d8b583e3bc0f4a22a02cc521e9990734,
title = "Removable sets for intrinsic metric and for holomorphic functions",
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.",
author = "Sergei Kalmykov and Kovalev, {Leonid V.} and Tapio Rajala",
note = "Funding Information: 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. publisher-imprint-name Hebrew University Magnes Press article-contains-esm No article-numbering-style Unnumbered article-registration-date-year 2024 article-registration-date-month 11 article-registration-date-day 7 article-toc-levels 0 journal-product ArchiveJournal numbering-style Unnumbered article-grants-type Regular metadata-grant OpenAccess abstract-grant OpenAccess bodypdf-grant Restricted bodyhtml-grant Restricted bibliography-grant Restricted esm-grant OpenAccess online-first true pdf-file-reference BodyRef/PDF/11854_2024_Article_76.pdf target-type OnlinePDF article-type OriginalPaper journal-subject-primary Mathematics journal-subject-secondary Analysis journal-subject-secondary Functional Analysis journal-subject-secondary Dynamical Systems and Ergodic Theory journal-subject-secondary Abstract Harmonic Analysis journal-subject-secondary Partial Differential Equations journal-subject-collection Mathematics and Statistics open-access false First 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. Publisher Copyright: {\textcopyright} 2019, The Hebrew University of Jerusalem.",
year = "2019",
month = oct,
day = "1",
doi = "10.1007/s11854-024-0076-2",
language = "English (US)",
volume = "139",
pages = "751--772",
journal = "Journal d'Analyse Mathematique",
issn = "0021-7670",
publisher = "Springer New York",
number = "2",
}