Ricci flow from spaces with isolated conical singularities

Gianniotis, Panagiotis¹ ; Schulze, Felix²

¹ Department of Mathematics, University of Toronto, Toronto, ON, Canada
² Department of Mathematics, University College London, London, United Kingdom

Geometry & topology, Tome 22 (2018) no. 7, pp. 3925-3977.

Résumé

Let $\left(M,g_0\right)$ be a compact $n$–dimensional Riemannian manifold with a finite number of singular points, where the metric is asymptotic to a nonnegatively curved cone over $\left({\mathbb{S}}^{n-1},g\right)$. We show that there exists a smooth Ricci flow starting from such a metric with curvature decaying like $C∕t$. The initial metric is attained in Gromov–Hausdorff distance and smoothly away from the singular points. In the case that the initial manifold has isolated singularities asymptotic to a nonnegatively curved cone over $\left({\mathbb{S}}^{n-1}∕\Gamma ,g\right)$, where $\Gamma$ acts freely and properly discontinuously, we extend the above result by showing that starting from such an initial condition there exists a smooth Ricci flow with isolated orbifold singularities.

Détail

DOI : 10.2140/gt.2018.22.3925

Classification : 53C44, 58J47
Keywords: Ricci flow, singular initial data, conical singularities

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