Existence of Ricci flows of incomplete surfaces

TL;DR

This paper proves the existence of Ricci flows on incomplete surfaces with unbounded curvature, providing explicit formulas for maximal existence time and describing asymptotic behavior.

Contribution

It establishes a general existence theorem for instantaneously complete Ricci flows on incomplete surfaces, including explicit maximal existence time formulas.

Findings

Existence of Ricci flows on incomplete surfaces with unbounded curvature.

Explicit formula for maximal existence time.

Description of asymptotic behavior in most cases.

Abstract

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.