On splitting complete manifolds via infinity harmonic functions
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917801521840128 |
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| author | Araújo, Damião J. Magliaro, Marco Mari, Luciano Pessoa, Leandro F. |
| author_facet | Araújo, Damião J. Magliaro, Marco Mari, Luciano Pessoa, Leandro F. |
| contents | In this paper, we prove some splitting results for manifolds supporting a non-constant infinity harmonic function which has at most linear growth on one side. Manifolds with non-negative Ricci or sectional curvature are considered. In dimension 2, we extend Savin's theorem on Lipschitz infinity harmonic functions in the plane to every surface with non-negative sectional curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07877 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On splitting complete manifolds via infinity harmonic functions Araújo, Damião J. Magliaro, Marco Mari, Luciano Pessoa, Leandro F. Differential Geometry Analysis of PDEs In this paper, we prove some splitting results for manifolds supporting a non-constant infinity harmonic function which has at most linear growth on one side. Manifolds with non-negative Ricci or sectional curvature are considered. In dimension 2, we extend Savin's theorem on Lipschitz infinity harmonic functions in the plane to every surface with non-negative sectional curvature. |
| title | On splitting complete manifolds via infinity harmonic functions |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2310.07877 |