Optimal maps and local-to-global property in negative dimensional spaces with Ricci curvature bounded from below

Chiara Rigoni; Mattia Magnabosco

Optimal maps and local-to-global property in negative dimensional spaces with Ricci curvature bounded from below

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arxiv 2105.12017 v1 pith:TOWPHGBS submitted 2021-05-25 math.DG math.FAmath.MG

Mattia Magnabosco , Chiara Rigoni This is my paper · ORCID

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In this paper we investigate two important properties of metric measure spaces satisfying the reduced curvature-dimension condition for negative values of the dimension parameter: the existence of a transport map between two suitable marginals and the so-called local-to-global property.

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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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