In this work we are going to establish Hölder continuity of harmonic maps from an open set Ω in an RCD(K,N) space valued into a CAT(κ) space, with the constraint that the image of Ω 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.
Comments on the Regularity of Harmonic Maps Between Singular Spaces / Gennaioli, L., Gigli, N., Zhang, H., Zhu, X.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 36:6(2026). [10.1007/s12220-026-02448-3]
Comments on the Regularity of Harmonic Maps Between Singular Spaces
Gennaioli, Luca;Gigli, Nicola;
2026-01-01
Abstract
In this work we are going to establish Hölder continuity of harmonic maps from an open set Ω in an RCD(K,N) space valued into a CAT(κ) space, with the constraint that the image of Ω 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.| File | Dimensione | Formato | |
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