Ricci flow from spaces with edge type conical singularities
Differential Geometry
2025-07-11 v2 Analysis of PDEs
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 for which converges back to the singular space as 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.
Keywords
Cite
@article{arxiv.2305.00344,
title = {Ricci flow from spaces with edge type conical singularities},
author = {Lucas Lavoyer},
journal= {arXiv preprint arXiv:2305.00344},
year = {2025}
}
Comments
Final version, accepted at Communications in Analysis and Geometry