Quasi-Continuous Vector Fields on RCD Spaces
Debin, C., Gigli, N., & Pasqualetto, E. (2021). Quasi-Continuous Vector Fields on RCD Spaces. Potential Analysis, 54(1), 183-211. https://doi.org/10.1007/s11118-019-09823-6
Published inPotential Analysis
© Springer Nature B.V. 2020
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.
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Additional information about fundingThis research has been supported by the MIUR SIR-grant ‘Nonsmooth Differential Geometry’ (RBSI147UG4).
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