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

Calculus of Variations and Geometric Measure Theory

L. Gennaioli

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

created by gennaioli on 29 Jul 2026

[BibTeX]

Preprint

Inserted: 29 jul 2026
Last Updated: 29 jul 2026

Year: 2026

Abstract:

We are going to prove that energy minimizing harmonic maps from a domain $\Omega$ inside an ${\rm RCD}(K,N)$ whose image lies in a small ball inside a ${\rm CAT}(\kappa)$ space are locally Lipschitz continuous. This completes the picture concerning regularity of harmonic maps between singular spaces and justifies a variant of the Bochner-Eells-Sampson inequality between singular spaces.

Download:

Lipschitz_continuity .pdf