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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.10932 |
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| _version_ | 1866914323021955072 |
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| author | Frenck, Georg Hanke, Bernhard Hirsch, Sven |
| author_facet | Frenck, Georg Hanke, Bernhard Hirsch, Sven |
| contents | We prove a Riemannian positive mass theorem for asymptotically flat spin manifolds with hypersurface singularities. Unlike earlier results, some components of the singular set may be mean-concave, provided that other components of the singular set are sufficiently mean-convex. Our proof uses initial data sets where a suitably chosen second fundamental form transfers convexity defects between different singularity components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10932 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The lock principle for scalar curvature Frenck, Georg Hanke, Bernhard Hirsch, Sven Differential Geometry Mathematical Physics We prove a Riemannian positive mass theorem for asymptotically flat spin manifolds with hypersurface singularities. Unlike earlier results, some components of the singular set may be mean-concave, provided that other components of the singular set are sufficiently mean-convex. Our proof uses initial data sets where a suitably chosen second fundamental form transfers convexity defects between different singularity components. |
| title | The lock principle for scalar curvature |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2602.10932 |