Ricci flow on surfaces with conical singularities, II

TL;DR

This paper investigates the behavior of the normalized Ricci flow on surfaces with conical singularities, establishing long-term existence for small cone angles and convergence under certain topological conditions.

Contribution

It extends Ricci flow analysis to surfaces with conical singularities, providing existence and convergence results for specific geometric and topological settings.

Findings

Long time existence for cone angles less than 2π.

Convergence results when the Euler number is nonpositive.

Analysis of Ricci flow behavior on singular surfaces.

Abstract

In this paper, we study the (normalized) Ricci flow on surfaces with conical singularities. Long time existence is proved for cone angle smaller than $2\pi$. In this case, convergence results are obtained if the Euler number is nonpositive.