Llarull's theorem on odd dimensional manifolds: the noncompact case
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911856887595008 |
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| author | Li, Yihan Su, Guangxiang Wang, Xiangsheng Zhang, Weiping |
| author_facet | Li, Yihan Su, Guangxiang Wang, Xiangsheng Zhang, Weiping |
| contents | Let $(M,g^{TM})$ be an odd dimensional ($\dim M\geq 3$) connected oriented noncompact complete spin Riemannian manifold. Let $k^{TM}$ be the associated scalar curvature. Let $f:M\to S^{\dim M}(1)$ be a smooth area decreasing map which is locally constant near infinity and of nonzero degree. Suppose $k^{TM}\geq ({\dim M})({\dim M}-1)$ on the support of ${\rm d}f$, we show that $\inf(k^{TM})<0$. This answers a question of Gromov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Llarull's theorem on odd dimensional manifolds: the noncompact case Li, Yihan Su, Guangxiang Wang, Xiangsheng Zhang, Weiping Differential Geometry Let $(M,g^{TM})$ be an odd dimensional ($\dim M\geq 3$) connected oriented noncompact complete spin Riemannian manifold. Let $k^{TM}$ be the associated scalar curvature. Let $f:M\to S^{\dim M}(1)$ be a smooth area decreasing map which is locally constant near infinity and of nonzero degree. Suppose $k^{TM}\geq ({\dim M})({\dim M}-1)$ on the support of ${\rm d}f$, we show that $\inf(k^{TM})<0$. This answers a question of Gromov. |
| title | Llarull's theorem on odd dimensional manifolds: the noncompact case |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2404.18153 |