Uniqueness of solutions of Ricci flow on complete noncompact manifolds

Abstract

We prove the uniqueness of solutions of the Ricci flow on complete noncompact manifolds with bounded curvatures using the De Turck approach. As a consequence we obtain a correct proof of the existence of solution of the Ricci harmonic flow on complete noncompact manifolds with bounded curvatures.

A simple example of a manifold with bounded curvature and injectivity radius going to zero as the point tends to infinity is given. A proof and argument why the crucial lemma Lemma 2.2 of the Chen-Zhu's paper \cite{CZ} cannot hold is given

References in corpus (1)

• A lower bound for the scalar curvature of the standard solution of the Ricci flow

Cited by in corpus (4)

• Gradient estimates for a nonlinear parabolic equation under Ricci flow
• Another proof of Ricci flow on incomplete surfaces with bounded above Gauss curvature
• Volume bounds of the Ricci flow on closed manifolds
• A pseudolocality theorem for Ricci flow