Ricci flow from singular spaces with bounded curvature

We show the existence of a solution to the Ricci flow with a compact length space of bounded curvature, i.e., a space that has curvature bounded above and below in the sense of Alexandrov, as its initial condition. We show that this flow converges in the $C^{1,\alpha}$-sense to a $C^{1,\alpha}$-continuous Riemannian manifold which is isometric to the original metric space. Moreover, we prove that the flow is uniquely determined by the initial condition, up to isometry.

Publication Details

Journal
ArXiv.org
Published
2025-03-07
Primary Topic
Geometric Analysis and Curvature Flows
Type
article
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article

Ricci flow from singular spaces with bounded curvature

ArXiv.org
Geometric Analysis and Curvature Flows
article

Ricci flow from singular spaces with bounded curvature

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Abstract

We show the existence of a solution to the Ricci flow with a compact length space of bounded curvature, i.e., a space that has curvature bounded above and below in the sense of Alexandrov, as its initial condition. We show that this flow converges in the $C^{1,\alpha}$-sense to a $C^{1,\alpha}$-continuous Riemannian manifold which is isometric to the original metric space. Moreover, we prove that the flow is uniquely determined by the initial condition, up to isometry.

ArXiv.org
Openalex Percentile: Top 39%
Geometric Analysis and Curvature Flows
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Ricci flow from singular spaces with bounded curvature · ArXiv.org (2025) | TGRS Research Map | TGRS