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.
Main Authors
Format
Articles
Research article
Published
2019
Series
Subjects
Publication in research information system
Publisher
Springer; Hebrew University Magnes Press
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201911124829Use this for linking
Review status
Peer reviewed
ISSN
0021-7670
DOI
https://doi.org/10.1007/s11854-024-0076-2
Language
English
Published in
Journal d'Analyse Mathématique
Citation
- Kalmykov, S., Kovalev, L. V., & Rajala, T. (2019). Removable sets for intrinsic metric and for holomorphic functions. Journal d'Analyse Mathématique, 139(2), 751-772. https://doi.org/10.1007/s11854-024-0076-2
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Funder(s)
Research Council of Finland
Funding program(s)
Academy Research Fellow, AoF
Akatemiatutkija, SA
Additional information about funding
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.
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