Positive scalar curvature on manifolds with boundary and their doubles
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929248853295104 |
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| author | Rosenberg, Jonathan Weinberger, Shmuel |
| author_facet | Rosenberg, Jonathan Weinberger, Shmuel |
| contents | This paper is about positive scalar curvature on a compact manifold $X$ with non-empty boundary $\partial X$. In some cases, we completely answer the question of when $X$ has a positive scalar curvature metric which is a product metric near $\partial X$, or when $X$ has a positive scalar curvature metric with positive mean curvature on the boundary, and more generally, we study the relationship between boundary conditions on $\partial X$ for positive scalar curvature metrics on $X$ and the positive scalar curvature problem for the double $M=\operatorname{Dbl}(X,\partial X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_01263 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Positive scalar curvature on manifolds with boundary and their doubles Rosenberg, Jonathan Weinberger, Shmuel Differential Geometry Algebraic Topology K-Theory and Homology 53C21 (Primary), 58J22, 53C27, 19L41, 55N22 (Secondary) This paper is about positive scalar curvature on a compact manifold $X$ with non-empty boundary $\partial X$. In some cases, we completely answer the question of when $X$ has a positive scalar curvature metric which is a product metric near $\partial X$, or when $X$ has a positive scalar curvature metric with positive mean curvature on the boundary, and more generally, we study the relationship between boundary conditions on $\partial X$ for positive scalar curvature metrics on $X$ and the positive scalar curvature problem for the double $M=\operatorname{Dbl}(X,\partial X)$. |
| title | Positive scalar curvature on manifolds with boundary and their doubles |
| topic | Differential Geometry Algebraic Topology K-Theory and Homology 53C21 (Primary), 58J22, 53C27, 19L41, 55N22 (Secondary) |
| url | https://arxiv.org/abs/2201.01263 |