The Ricci-DeTurck flow on complete manifolds
Differential Geometry
2026-03-25 v1
Abstract
Based on the framework of Koch-Lamm and tensor heat kernel estimates, we obtain a uniform proof of the short-time existence, uniqueness, and continuous dependence for Ricci flows starting from a complete Riemannian metric with bounded curvature. A new ingredient is an effective continuous dependence estimate without the assumption of injectivity radius lower bound.
Keywords
Cite
@article{arxiv.2603.22834,
title = {The Ricci-DeTurck flow on complete manifolds},
author = {Jing-Bin Cai and Bing Wang},
journal= {arXiv preprint arXiv:2603.22834},
year = {2026}
}