Llarull's theorem on punctured sphere with $L^\infty$ metric
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909215785746432 |
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| author | Chu, Jianchun Lee, Man-Chun Zhu, Jintian |
| author_facet | Chu, Jianchun Lee, Man-Chun Zhu, Jintian |
| contents | The classical Llarull theorem states that a smooth metric on $n$-sphere cannot have scalar curvature no less than $n(n-1)$ and dominate the standard spherical metric at the same time unless it is the standard spherical metric. In this work, we prove that Llarull's rigidity theorem holds for $L^{\infty}$ metrics on spheres with finitely many points punctured. This is related to a question of Gromov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Llarull's theorem on punctured sphere with $L^\infty$ metric Chu, Jianchun Lee, Man-Chun Zhu, Jintian Differential Geometry Metric Geometry The classical Llarull theorem states that a smooth metric on $n$-sphere cannot have scalar curvature no less than $n(n-1)$ and dominate the standard spherical metric at the same time unless it is the standard spherical metric. In this work, we prove that Llarull's rigidity theorem holds for $L^{\infty}$ metrics on spheres with finitely many points punctured. This is related to a question of Gromov. |
| title | Llarull's theorem on punctured sphere with $L^\infty$ metric |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2405.19724 |