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Quasi-continuous vector fields on RCD spaces

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arxiv 1903.04302 v2 pith:DD2HGY7B submitted 2019-03-11 math.FA

Clément Debin , Nicola Gigli , Enrico Pasqualetto This is my paper · ORCID
classification math.FA
keywords definedfieldstensorcapacity-aquasi-continuousspacesvectorcalculus
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces

    math.MG 2019-09 conditional novelty 7.0 of 10

    In RCD(K,N) spaces, the reduced boundary of a set of finite perimeter has a unique Euclidean half-space tangent at almost every point and is rectifiable by bi-Lipschitz charts.

  2. Lipschitz continuity of harmonic maps between ${\rm RCD}(K,N)$ spaces and ${\rm CAT}(\kappa)$ spaces

    math.AP 2026-07 accept novelty 5.0 of 10

    Energy-minimizing harmonic maps from RCD(K,N) domains into small balls in CAT(κ) spaces are locally Lipschitz, completing the singular Bochner–Eells–Sampson picture.

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