Ricci flow from spaces with isolated conical singularities

Understand

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.