Integral curvature estimates for solutions to Ricci flow with L^p bounded scalar curvature

2024/06/04 by Jiawei Liu, Liu, Jiawei, Miles Simon +1
Mathematics · Physics and Astronomy · #53C21 #53E20 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2406.02351

openalex publication_date 2024/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper we prove localised weighted curvature integral estimates for solutions to the Ricci flow in the setting of a smooth four dimensional Ricci flow or a closed n-dimensional Kähler Ricci flow. These integral estimates improve and extend the integral curvature estimates shown by the second author in an earlier paper. If the scalar curvature is uniformly bounded in the spatial L^p sense for some p>2, then the estimates imply a uniform bound on the spatial L² norm of the Riemannian curvature tensor. Stronger integral estimates are shown to hold if one further assumes a weak non-inflating condition, or we restrict to closed manifolds.

Related

• Curvature Estimates for the Ricci Flow I
• Volume estimates and convergence results for solutions to Ricci flow with L^p bounded scalar curvature
• Curvature Estimates for the Ricci Flow II
• Some integral curvature estimates for the Ricci flow in four dimensions
• Local curvature estimates for the Ricci-harmonic flow