Communications in Analysis and Geometry

Volume 30 (2022)

Number 10

Improved pseudolocality on large hyperbolic balls

Pages: 2285 – 2314



Andrew D. McLeod (Mathematical Institute, University of Oxford, United Kingdom)


We obtain an improved pseudolocality result for Ricci flows on two-dimensional surfaces that are initially almost-hyperbolic on large hyperbolic balls. We prove that, at the central point of the hyperbolic ball, the Gauss curvature remains close to the hyperbolic value for a time that grows exponentially in the radius of the ball. This two-dimensional result allows us to precisely conjecture how the phenomenon should appear in the higher dimensional setting.

Received 11 December 2018

Accepted 1 July 2020

Published 29 September 2023