Ricci flow from spaces with isolated conical singularities

Abstract

Let $(M,g_0)$ be a compact $n$-dimensional Riemannian manifold with a finite number of singular points, where the metric is asymptotic to a non-negatively curved cone over $({\mathbb{S}}^{n-1},g)$. 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 non-negatively curved cone over $({\mathbb{S}}^{n-1}/\Gamma ,g)$, 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.

Final version, to appear in Geometry & Topology

References in corpus (2)

• Ricci flow on Orbifold
• Smoothing 3-dimensional polyhedral spaces

Cited by in corpus (5)

• New expanding Ricci solitons starting in dimension four
• Ricci flow from some spaces with asymptotically cylindrical singularities
• Perelman's functionals on cones and Construction of type III Ricci flows coming out of cones
• Ends of (singular) Ricci shrinkers
• Ricci Flow recovering from pinched discs