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Quasi-Continuous Vector Fields on RCD Spaces

Abstract
In the existing language for tensor calculus on RCD spaces, tensor fields are only defined m-a.e.. In this paper we introduce the concept of tensor field defined ‘2-capacity-a.e.’ and discuss in which sense Sobolev vector fields have a 2-capacity-a.e. uniquely defined quasi-continuous representative.
Main Authors
Debin, Clément Gigli, Nicola Pasqualetto, Enrico
Format
Articles Research article
Published
2021
Series
Potential Analysis
Subjects
RCD space
differential calculus
quasi-continuity
differentiaaligeometria
funktionaalianalyysi
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/34664253
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202003032258Use this for linking
Review status
Peer reviewed
ISSN
0926-2601
DOI
https://doi.org/10.1007/s11118-019-09823-6
Language
English
Published in
Potential Analysis
Citation
License
In CopyrightOpen Access
Additional information about funding
This research has been supported by the MIUR SIR-grant ‘Nonsmooth Differential Geometry’ (RBSI147UG4).
Copyright© Springer Nature B.V. 2020

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