Positive mass and Dirac operators on weighted manifolds and smooth metric measure spaces
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909124578508800 |
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| author | Law, Michael B. Lopez, Isaac M. Santiago, Daniel |
| author_facet | Law, Michael B. Lopez, Isaac M. Santiago, Daniel |
| contents | We establish a weighted positive mass theorem which unifies and generalizes results of Baldauf--Ozuch and Chu--Zhu. Our result is in fact equivalent to the usual positive mass theorem, and can be regarded as a positive mass theorem for smooth metric measure spaces. We also study Dirac operators on certain warped product manifolds associated to smooth metric measure spaces. Applications of this include, among others, an alternative proof for a special case of our positive mass theorem, eigenvalue bounds for the Dirac operator on closed spin manifolds, and a new way to understand the weighted Dirac operator using warped products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15441 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Positive mass and Dirac operators on weighted manifolds and smooth metric measure spaces Law, Michael B. Lopez, Isaac M. Santiago, Daniel Differential Geometry Mathematical Physics We establish a weighted positive mass theorem which unifies and generalizes results of Baldauf--Ozuch and Chu--Zhu. Our result is in fact equivalent to the usual positive mass theorem, and can be regarded as a positive mass theorem for smooth metric measure spaces. We also study Dirac operators on certain warped product manifolds associated to smooth metric measure spaces. Applications of this include, among others, an alternative proof for a special case of our positive mass theorem, eigenvalue bounds for the Dirac operator on closed spin manifolds, and a new way to understand the weighted Dirac operator using warped products. |
| title | Positive mass and Dirac operators on weighted manifolds and smooth metric measure spaces |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2312.15441 |