A scalar-mean curvature comparison theorem for manifolds with iterated conical singularities
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916817545461760 |
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| author | Jovanovic, Milan Wang, Jinmin |
| author_facet | Jovanovic, Milan Wang, Jinmin |
| contents | We use the Dirac operator method to prove a scalar-mean curvature comparison theorem for spin manifolds which carry iterated conical singularities. Our approach is to study the index theory of a twisted Dirac operator on such singular manifolds. A dichotomy argument is used to prove the comparison theorem without knowing precisely the index of the twisted Dirac operator. This framework also enables us to prove a rigidity theorem of Euclidean domains and a spin positive mass theorem for asymptotically flat manifolds with iterated conical singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_24059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A scalar-mean curvature comparison theorem for manifolds with iterated conical singularities Jovanovic, Milan Wang, Jinmin Differential Geometry We use the Dirac operator method to prove a scalar-mean curvature comparison theorem for spin manifolds which carry iterated conical singularities. Our approach is to study the index theory of a twisted Dirac operator on such singular manifolds. A dichotomy argument is used to prove the comparison theorem without knowing precisely the index of the twisted Dirac operator. This framework also enables us to prove a rigidity theorem of Euclidean domains and a spin positive mass theorem for asymptotically flat manifolds with iterated conical singularities. |
| title | A scalar-mean curvature comparison theorem for manifolds with iterated conical singularities |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2506.24059 |