A1 Journal article (refereed)
Removable sets for intrinsic metric and for holomorphic functions (2019)

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

JYU authors or editors

Rajala, Tapio

Publication details

All authors or editors: Kalmykov, Sergei; Kovalev, Leonid V.; Rajala, Tapio

Journal or series: Journal d'Analyse Mathématique

ISSN: 0021-7670

eISSN: 1565-8538

Publication year: 2019

Volume: 139

Issue number: 2

Pages range: 751-772

Publisher: Springer; Hebrew University Magnes Press

Publication country: Israel

Publication language: English

DOI: https://doi.org/10.1007/s11854-024-0076-2

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/66319

Publication is parallel published: https://arxiv.org/pdf/1707.07363.pdf

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.

Keywords: metric spaces; mathematics

Free keywords: intrinsic metrics; holomorphic functions

Fields of science: