Long time existence and bounded scalar curvature in the Ricci-harmonic flow

Abstract

In this paper we study the long time existence of the Ricci-harmonic flow in terms of scalar curvature and Weyl tensor which extends Cao's result \cite{Cao2011} in the Ricci flow. In dimension four, we also study the integral bound of the "Riemann curvature" for the Ricci-harmonic flow generalizing a recently result of Simon \cite{Simon2015}.

24 pages

References in corpus (4)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• On Type I Singularities in Ricci flow
• A Gaussian upper bound of the conjugate heat equation along an extended Ricci flow
• An upper bound of the heat kernel along the harmonic-Ricci flow