Stability of Llarull's theorem in all dimensions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914801285857280 |
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| author | Hirsch, Sven Zhang, Yiyue |
| author_facet | Hirsch, Sven Zhang, Yiyue |
| contents | Llarull's theorem characterizes the round sphere $S^n$ among all spin manifolds whose scalar curvature is bounded from below by $n(n-1)$. In this paper we show that if the scalar curvature is bounded from below by $n(n-1)-\varepsilon$, the underlying manifold is $C^0$-close to a finite number of spheres outside a small bad set. This completely solves Gromov's spherical stability problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_14412 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability of Llarull's theorem in all dimensions Hirsch, Sven Zhang, Yiyue Differential Geometry Analysis of PDEs 53C27, 53C24 Llarull's theorem characterizes the round sphere $S^n$ among all spin manifolds whose scalar curvature is bounded from below by $n(n-1)$. In this paper we show that if the scalar curvature is bounded from below by $n(n-1)-\varepsilon$, the underlying manifold is $C^0$-close to a finite number of spheres outside a small bad set. This completely solves Gromov's spherical stability problem. |
| title | Stability of Llarull's theorem in all dimensions |
| topic | Differential Geometry Analysis of PDEs 53C27, 53C24 |
| url | https://arxiv.org/abs/2310.14412 |