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arXiv · 2408.00479

Comments on the regularity of harmonic maps between singular spaces

Luca Gennaioli·Nicola Gigli·Hui-Chun Zhang·Xi-Ping Zhu
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Abstract

In this work we are going to establish H\"older continuity of harmonic maps from an open set $\Omega$ in an ${\rm RCD}(K,N)$ space valued into a ${\rm CAT}(\kappa)$ space, with the constraint that the image of $\Omega$ via the map is contained in a sufficiently small ball in the target. Building on top of this regularity and assuming a local Lipschitz regularity of the map, we establish a weak version of the Bochner-Eells-Sampson inequality in such a non-smooth setting. Finally we study the boundary regularity of such maps.

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Luca Gennaioli, Nicola Gigli, Hui-Chun Zhang, Xi-Ping Zhu. 2024-08-01. Comments on the regularity of harmonic maps between singular spaces. https://arxiv.org/abs/2408.00479

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