Interior control for surfaces with positive scalar curvature and its application
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911324598960128 |
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| author | Chen, Shuli Chu, Jianchun Zhu, Jintian |
| author_facet | Chen, Shuli Chu, Jianchun Zhu, Jintian |
| contents | Let $M^{n}$, $n\in\{3,4,5\}$, be a closed aspherical $n$-manifold and $S\subset M$ a subset consisting of disjoint incompressible embedded closed aspherical submanifolds (possibly with different dimensions). When $n =3,4$, we show that $M\setminus S$ cannot admit any complete metric with positive scalar curvature. When $n=5$, we obtain the same result when $S$ contains a submanifold of codimension 1 or 2. The key ingredient is a new interior control for the extrinsic diameter of surfaces with positive scalar curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interior control for surfaces with positive scalar curvature and its application Chen, Shuli Chu, Jianchun Zhu, Jintian Differential Geometry 53C21, 53A10 Let $M^{n}$, $n\in\{3,4,5\}$, be a closed aspherical $n$-manifold and $S\subset M$ a subset consisting of disjoint incompressible embedded closed aspherical submanifolds (possibly with different dimensions). When $n =3,4$, we show that $M\setminus S$ cannot admit any complete metric with positive scalar curvature. When $n=5$, we obtain the same result when $S$ contains a submanifold of codimension 1 or 2. The key ingredient is a new interior control for the extrinsic diameter of surfaces with positive scalar curvature. |
| title | Interior control for surfaces with positive scalar curvature and its application |
| topic | Differential Geometry 53C21, 53A10 |
| url | https://arxiv.org/abs/2502.14216 |