On a Rigidity Result in Positive Scalar Curvature Geometry
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914221470515200 |
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| author | Mondal, Puskar |
| author_facet | Mondal, Puskar |
| contents | I prove a scalar curvature rigidity theorem for spheres. In particular, I prove that geodesic balls of radii strictly less than $\fracπ{2}$ in $n+1~(n\geq 2)$ dimensional unit sphere can be rigid under smooth deformations that increase scalar curvature preserving the intrinsic geometry and the mean curvature of the boundary, and such rigidity result fails for the hemisphere. The proof of this assertion requires the notion of a real Killing connection and solution of the boundary value problem associated with its Dirac operator. The result serves as the sharpest refinement of the now-disproven Min-Oo conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23406 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Rigidity Result in Positive Scalar Curvature Geometry Mondal, Puskar Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics I prove a scalar curvature rigidity theorem for spheres. In particular, I prove that geodesic balls of radii strictly less than $\fracπ{2}$ in $n+1~(n\geq 2)$ dimensional unit sphere can be rigid under smooth deformations that increase scalar curvature preserving the intrinsic geometry and the mean curvature of the boundary, and such rigidity result fails for the hemisphere. The proof of this assertion requires the notion of a real Killing connection and solution of the boundary value problem associated with its Dirac operator. The result serves as the sharpest refinement of the now-disproven Min-Oo conjecture. |
| title | On a Rigidity Result in Positive Scalar Curvature Geometry |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2410.23406 |