Ricci flow on surfaces with conical singularities

Abstract

This paper studies the normalized Ricci flow on surfaces with conical singularities. It's proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes good geometric sense. For some simple surfaces of this kind, for example, the tear drop and the football, it's shown that they admit Ricci soliton metric.

There is no revision to the paper, just this comment. Recently I found a gap in the proof of Theorem 1.1. Please see Remark 1.2 of arXiv:1305.4355 for details

Cited by in corpus (4)

• Smooth approximations of the Conical Kahler-Ricci flows
• The Ricci flow on the sphere with marked points
• Perelman's $W$-functional on manifolds with conical singularities
• Ricci flow on cone surfaces and a three-dimensional expanding soliton