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arXiv · 2503.05896

Ricci flow from singular spaces with bounded curvature

Diego Corro·Masoumeh Zarei·Adam Moreno
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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.

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Diego Corro, Masoumeh Zarei, Adam Moreno. 2025-03-07. Ricci flow from singular spaces with bounded curvature. https://arxiv.org/abs/2503.05896

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