Liouville-Type Theorems on the Hyperbolic Space
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911756313427968 |
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| author | Lee, Sanghoon |
| author_facet | Lee, Sanghoon |
| contents | In this paper, we establish Liouville-type theorems for a one-parameter family of elliptic PDEs on the standard upper half-plane model of the hyperbolic space, under specific geometric assumptions. Our results indicate that the Euclidean half-plane is the only compactification of the hyperbolic space when the scalar curvature of the compactified metric has a designated sign. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06623 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Liouville-Type Theorems on the Hyperbolic Space Lee, Sanghoon Differential Geometry Analysis of PDEs In this paper, we establish Liouville-type theorems for a one-parameter family of elliptic PDEs on the standard upper half-plane model of the hyperbolic space, under specific geometric assumptions. Our results indicate that the Euclidean half-plane is the only compactification of the hyperbolic space when the scalar curvature of the compactified metric has a designated sign. |
| title | Liouville-Type Theorems on the Hyperbolic Space |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2401.06623 |