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

Luca Gennaioli

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arXiv · 2607.27010

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

Luca Gennaioli

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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.

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Luca Gennaioli. 2026-07-29. Lipschitz continuity of harmonic maps between ${\rm RCD}(K,N)$ spaces and ${\rm CAT}(\kappa)$ spaces. https://arxiv.org/abs/2607.27010

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