Analysis aspects of Ricci flow on conical surfaces

TL;DR

This paper develops a framework for analyzing the Ricci flow on conical surfaces, proving long-term existence and optimal regularity, including explicit asymptotic behavior near cone points.

Contribution

It introduces a new analytical framework for conical Ricci flow, establishing long-time existence and detailed regularity results for general cone angles.

Findings

Proves long-time existence of conical Ricci flow.

Shows boundedness of time derivatives of the conformal factor.

Provides explicit asymptotic expansion near cone points.

Abstract

In this paper, we establish a framework for the analysis of linear parabolic equations on conical surfaces and use them to study the conical Ricci flow. In particular, we prove the long time existence of the conical Ricci flow for general cone angle and show that this solution has the optimal regularity, namely, the time derivatives of the conformal factor are bounded and for each fixed time, the conformal factor has an explicit asymptotic expansion near the cone points.