Communications in Analysis and Geometry
Volume 30 (2022)
Improved pseudolocality on large hyperbolic balls
Pages: 2285 – 2314
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