English

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 (M,g(t))(M,g(t)) for t(0,T],t\in (0,T], which converges back to the singular space as t0t\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.

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

R2 v1 2026-06-28T10:21:42.430Z