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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.00479 |
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| _version_ | 1866929445949931520 |
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| author | Gennaioli, Luca Gigli, Nicola Zhang, Hui-Chun Zhu, Xi-Ping |
| author_facet | Gennaioli, Luca Gigli, Nicola Zhang, Hui-Chun Zhu, Xi-Ping |
| contents | In this work we are going to establish Hölder continuity of harmonic maps from an open set $Ω$ in an ${\rm RCD}(K,N)$ space valued into a ${\rm CAT}(κ)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00479 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comments on the regularity of harmonic maps between singular spaces Gennaioli, Luca Gigli, Nicola Zhang, Hui-Chun Zhu, Xi-Ping Analysis of PDEs Metric Geometry In this work we are going to establish Hölder continuity of harmonic maps from an open set $Ω$ in an ${\rm RCD}(K,N)$ space valued into a ${\rm CAT}(κ)$ 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. |
| title | Comments on the regularity of harmonic maps between singular spaces |
| topic | Analysis of PDEs Metric Geometry |
| url | https://arxiv.org/abs/2408.00479 |