A note on Ricci flow from small curvature concentration and a Morrey-type condition
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| Format: | Preprint |
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2026
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| _version_ | 1866911556016537600 |
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| author | Chau, Albert Martens, Adam |
| author_facet | Chau, Albert Martens, Adam |
| contents | In \cite{ChauMartens} the authors proved the long-time existence of Ricci flow starting from complete bounded curvature Riemannian manifolds with scale-invariant integral curvature bounded by a dimensional constant times the inverse of the Sobolev constant. We generalize this result by replacing the bounded curvature assumption with the assumption that $g$ is only equivalent to a complete bounded curvature metric $h$ while satisfying a Morrey-type condition on the gradient of $g$ relative to $h$: a local integral condition on the covariant derivative $\nabla_h g$. The Morrey-type condition was first considered in \cite{LeeLiu} in the context of Ricci flow on non-compact manifolds, and in particular allows the possibility for $g$ to have unbounded curvature on $M$. As in \cite{ChauMartens}, our long-time solution enjoys curvature decay estimates implying in particular that $M$ is diffeomorphic to $\mathbb{R}^n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_28976 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on Ricci flow from small curvature concentration and a Morrey-type condition Chau, Albert Martens, Adam Differential Geometry 53E20 In \cite{ChauMartens} the authors proved the long-time existence of Ricci flow starting from complete bounded curvature Riemannian manifolds with scale-invariant integral curvature bounded by a dimensional constant times the inverse of the Sobolev constant. We generalize this result by replacing the bounded curvature assumption with the assumption that $g$ is only equivalent to a complete bounded curvature metric $h$ while satisfying a Morrey-type condition on the gradient of $g$ relative to $h$: a local integral condition on the covariant derivative $\nabla_h g$. The Morrey-type condition was first considered in \cite{LeeLiu} in the context of Ricci flow on non-compact manifolds, and in particular allows the possibility for $g$ to have unbounded curvature on $M$. As in \cite{ChauMartens}, our long-time solution enjoys curvature decay estimates implying in particular that $M$ is diffeomorphic to $\mathbb{R}^n$. |
| title | A note on Ricci flow from small curvature concentration and a Morrey-type condition |
| topic | Differential Geometry 53E20 |
| url | https://arxiv.org/abs/2603.28976 |