Systolic inequalities and the Horowitz-Myers conjecture
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913576177893376 |
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| author | Brendle, S. Hung, P. K. |
| author_facet | Brendle, S. Hung, P. K. |
| contents | Let $n$ be an integer with $3 \leq n \leq 7$, and let $g$ be a Riemannian metric on $B^2 \times T^{n-2}$ with scalar curvature at least $-n(n-1)$. We establish an inequality relating the systole of the boundary to the infimum of the mean curvature on the boundary. As a consequence, we obtain a new positive energy theorem where equality holds for the Horowitz-Myers metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04283 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Systolic inequalities and the Horowitz-Myers conjecture Brendle, S. Hung, P. K. Differential Geometry Let $n$ be an integer with $3 \leq n \leq 7$, and let $g$ be a Riemannian metric on $B^2 \times T^{n-2}$ with scalar curvature at least $-n(n-1)$. We establish an inequality relating the systole of the boundary to the infimum of the mean curvature on the boundary. As a consequence, we obtain a new positive energy theorem where equality holds for the Horowitz-Myers metrics. |
| title | Systolic inequalities and the Horowitz-Myers conjecture |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2406.04283 |