Ricci flow of negatively curved incomplete surfaces

TL;DR

This paper proves the uniqueness of Ricci flows originating from negatively curved incomplete surfaces, assuming the flows become complete instantly, thereby establishing well-posedness for this class of geometric flows.

Contribution

It establishes the uniqueness of Ricci flows on negatively curved incomplete surfaces with instantaneous completeness, complementing existing existence results.

Findings

Uniqueness of Ricci flows in the specified setting

Well-posedness of Ricci flow for negatively curved incomplete surfaces

Flows become complete instantaneously

Abstract

We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more general existence result proved in [10], this settles the issue of well-posedness in this class.