Calculus of Variations and Geometric Measure Theory
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C. Debin - N. Gigli - E. Pasqualetto

Quasi-continuous vector fields on $\sf RCD$ spaces

created by pasqualetto on 13 Mar 2019

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Submitted Paper

Inserted: 13 mar 2019
Last Updated: 13 mar 2019

Year: 2019

Abstract:

In the existing language for tensor calculus on $\sf RCD$ 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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