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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Advanced Differential Geometry Research
Publication details
- Journal / source
- Communications in Analysis and Geometry
- Publisher
- International Press of Boston
- Volume
- 34
- Issue
- 1
- Pages
- 39–87
- Publication date
- 1 January 2026
- Language
- EN