Curve shortening flows in warped product manifolds

2015/11/24 by Zhou, Hengyu
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.07553

Abstract

We study curve shortening flows in two types of warped product manifolds. These manifolds are S¹× N with two types of warped metrics where S¹ is the unit circle in R² and N is a closed Riemannian manifold. If the initial curve is a graph over S¹, then its curve shortening flow exists for all times and finally converges to a geodesic closed curve.

Related

• Mean curvature flows of graphs sliding off to infinity in warped product manifolds
• Curve shortening flows on surfaces that are not convex at infinity
• Curve Shortening Flow in a Riemannian Manifold
• Mean Curvature Flows of Closed Hypersurfaces in Warped Product Manifolds
• Mean curvature flow of graphs in warped products