Convergence stability for Ricci flow on manifolds with bounded geometry
Abstract
We prove that the Ricci flow for complete metrics with bounded geometry depends continuously on initial conditions for finite time with no loss of regularity. This relies on our recent work where sectoriality for the generator of the Ricci-DeTurck flow is proved. We use this to prove that for initial metrics sufficiently close in H\"older norm to a rotationally symmetric asymptotically hyperbolic metric and satisfying a simple curvature condition, but a priori distant from the hyperbolic metric, Ricci flow converges to the hyperbolic metric.
Cite
@article{arxiv.2303.04800,
title = {Convergence stability for Ricci flow on manifolds with bounded geometry},
author = {Eric Bahuaud and Christine Guenther and James Isenberg and Rafe Mazzeo},
journal= {arXiv preprint arXiv:2303.04800},
year = {2024}
}
Comments
11 pages. This revision clarifies one argument in our published article appearing in the Proceedings of the American Mathematical Society. There are small modifications to the statements of several Theorems