Communications in Analysis and Geometry

Volume 28 (2020)

Number 5

Rate of curvature decay for the contracting cusp Ricci flow

Pages: 1221 – 1250



Peter M. Topping (Mathematics Institute, University of Warwick, Coventry, United Kingdom)

Hao Yin (School of Mathematical Sciences, University of Science and Technology of China, Hefei, China)


We prove that the Ricci flow that contracts a hyperbolic cusp has curvature decay $\operatorname{max} K \sim \frac{1}{t^2}$. In order to do this, we prove a new Li–Yau type differential Harnack inequality for Ricci flow.

Received 6 November 2016

Accepted 4 February 2018

Published 14 October 2020