Ricci flow from spaces with edge type conical singularities

Abstract

We study the Ricci flow out of spaces with edge type conical singularities along a closed, embedded curve. Under the additional assumption that for each point of the curve, our space is locally modelled on the product of a fixed positively curved cone and a line, we show existence of a solution to Ricci flow $(M,g(t))$ for $t\in (0,T],$ which converges back to the singular space as $t\searrow 0$ in the pointed Gromov-Hausdorff topology. We also prove curvature estimates for the solution and, for edge points, we show that the tangent flow at these points is a positively curved expanding Ricci soliton solution crossed with a line.

Final version, accepted at Communications in Analysis and Geometry