Smooth long-time existence of Harmonic Ricci Flow on surfaces

TL;DR

This paper proves that for the Harmonic Ricci Flow on surfaces, singularities involve simultaneous blow-up of energy density and curvature, leading to conditions for long-time smooth existence.

Contribution

It establishes conditions under which the Harmonic Ricci Flow on surfaces exists smoothly for all time, especially with large coupling constants.

Findings

Energy density and curvature blow up simultaneously at singularities

Long-time existence is guaranteed for large coupling constants

Provides insight into singularity formation in Harmonic Ricci Flow

Abstract

We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain manifold have to blow up simultaneously. As an immediate consequence, we obtain smooth long-time existence for the Harmonic Ricci Flow with large coupling constant.