Gap phenomenon for scalar curvature
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913633504591872 |
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| author | Sun, Yukai Wang, Changliang |
| author_facet | Sun, Yukai Wang, Changliang |
| contents | Inspired by Goette-Semmelmann \cite{GSSU2002}, we derive an estimate for the scalar curvature without a nonnegativity assumption on curvature operator. As an application, we show that, on an even dimensional closed manifold with nonzero Euler characteristic, any Riemannian metric $g$ is $ε$-gap distance extremal for some $ε\geq 0$. For manifolds with boundary, inspired by Lott \cite{JL2021}, we obtained a similar estimate for scalar curvature and mean curvature. We apply the estimate on certain Euclidean domains to study a Gromov's question in \cite{GM20233} concerning the extension problem of metric on the boundary to the interior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gap phenomenon for scalar curvature Sun, Yukai Wang, Changliang Differential Geometry Inspired by Goette-Semmelmann \cite{GSSU2002}, we derive an estimate for the scalar curvature without a nonnegativity assumption on curvature operator. As an application, we show that, on an even dimensional closed manifold with nonzero Euler characteristic, any Riemannian metric $g$ is $ε$-gap distance extremal for some $ε\geq 0$. For manifolds with boundary, inspired by Lott \cite{JL2021}, we obtained a similar estimate for scalar curvature and mean curvature. We apply the estimate on certain Euclidean domains to study a Gromov's question in \cite{GM20233} concerning the extension problem of metric on the boundary to the interior. |
| title | Gap phenomenon for scalar curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.01252 |