Rate of curvature decay for the contracting cusp Ricci flow

TL;DR

This paper establishes that the Ricci flow contracting a hyperbolic cusp exhibits curvature decay proportional to one over time squared, supported by a new differential Harnack inequality for surface Ricci flows.

Contribution

It introduces a novel Li-Yau type differential Harnack inequality for Ricci flow on surfaces, enabling precise curvature decay estimates.

Findings

Curvature decays like 1 over time squared during cusp contraction.

New Li-Yau type inequality for Ricci flow on surfaces.

Provides a quantitative rate of curvature decay for hyperbolic cusp Ricci flow.

Abstract

We prove that the Ricci flow that contracts a hyperbolic cusp has curvature decay like one over time squared. In order to do this, we prove a new Li-Yau type differential Harnack inequality for Ricci flow on surfaces.