Long Time Existence of the Cross Curvature Flow in 3-Manifolds with Negative Sectional Curvature

2016/08/23 by Wei-Hung Liao, Liao, Wei-Hung
Computer Science · Mathematics · #53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1608.06599

openalex publication_date 2016/08/23 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

Abstract

Given a closed 3-manifold with an initial Riemannian metric of negative sec- tional curvature, we consider the cross curvature flow an evolution equation of metric on M3. We prove long-time existence of a solution to the cross curvature flow via the maximum principle theorem. Besides, we demonstrate the solution exists for all time and converges pointwisely to a hyperbolic metric

Related

• The Cross Curvature Flow of 3-manifolds with Negative Sectional Curvature
• Cross Curvature Flow on Locally Homogenous Three-manifolds (I)
• Generalized cross curvature flow
• Cross Curvature Flow on Locally Homogeneous Three-manifolds (II)
• Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric