Rigidity of the gradient estimate for Einstein manifolds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911307089838080 |
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| author | Lee, Sanghoon Park, Jiewon |
| author_facet | Lee, Sanghoon Park, Jiewon |
| contents | We study the rigidity of Ricci-flat manifolds with quadratic curvature decay under conditions on the Green function. We show that if the gradient of the Green function is uniformly bounded from below, then the manifold is flat. Furthermore, we prove that for a Ricci-flat manifold with quadratic curvature decay and Euclidean volume growth, the curvature is in $L^p$ for any $p \ge 2$. Combining with Cheeger-Tian \cite{CT} and Kröncke-Szabó \cite{KS}, we obtain that the manifold must be ALE of optimal order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07278 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of the gradient estimate for Einstein manifolds Lee, Sanghoon Park, Jiewon Differential Geometry We study the rigidity of Ricci-flat manifolds with quadratic curvature decay under conditions on the Green function. We show that if the gradient of the Green function is uniformly bounded from below, then the manifold is flat. Furthermore, we prove that for a Ricci-flat manifold with quadratic curvature decay and Euclidean volume growth, the curvature is in $L^p$ for any $p \ge 2$. Combining with Cheeger-Tian \cite{CT} and Kröncke-Szabó \cite{KS}, we obtain that the manifold must be ALE of optimal order. |
| title | Rigidity of the gradient estimate for Einstein manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.07278 |