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

2015/10/20 by Yi Li, Li, Yi
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1510.05788

24 pages

openalex publication_date 2015/10/20 · arxiv created 2015/11/27 · arxiv updated 2015/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeCao2011 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 \citeSimon2015.

Citations

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• An upper bound of the heat kernel along the harmonic-Ricci flow

Related

• Local curvature estimates for the Ricci-harmonic flow
• Short-time persistence of bounded curvature under the Ricci flow
• Curvature tensor under the Ricci-Harmonic flow
• Curvature Estimates for the Ricci Flow II
• On the conditions to extend Ricci flow(III)