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

Luca Gennaioli

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

Analysis of PDEs 2026-07-29 v1

Authors: Luca Gennaioli

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.

Keywords

harmonic maps RCD spaces CAT spaces Lipschitz continuity regularity

Cite

@article{arxiv.2607.27010,
  title  = {Lipschitz continuity of harmonic maps between ${\rm RCD}(K,N)$ spaces and ${\rm CAT}(κ)$ spaces},
  author = {Luca Gennaioli},
  journal= {arXiv preprint arXiv:2607.27010},
  year   = {2026}
}

Comments

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