Abstract
In the existing language for tensor calculus on RCD spaces, tensor fields are only defined \(\mathfrak {m}\)-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.
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Acknowledgments
This research has been supported by the MIUR SIR-grant ‘Nonsmooth Differential Geometry’ (RBSI147UG4). The authors want to thank Elia Bruè and Daniele Semola for stimulating conversations on the topics of this manuscript.
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Debin, C., Gigli, N. & Pasqualetto, E. Quasi-Continuous Vector Fields on RCD Spaces. Potential Anal 54, 183–211 (2021). https://doi.org/10.1007/s11118-019-09823-6
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DOI: https://doi.org/10.1007/s11118-019-09823-6