Collapsing of Mean Curvature Flow of Hypersurfaces to Complex Submanifolds

2023/09/08 by Ghanbari, Farnaz, Samreena
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.04176

Abstract

In this paper, we produce explicit examples of mean curvature flow of (2m-1)-dimensional submanifolds which converge to (2m-2)-dimensional submanifolds at a finite time. These examples are a special class of hyperspheres in ℂ^m with a U(m)-invariant Kähler metrics. We first discuss the mean curvature flow problem and then investigate the type of singularities for them.

Related

• The mean curvature flow of submanifolds of high codimension
• Mean Curvature Flow of Higher Codimension in Hyperbolic Spaces
• The mean curvature flow by parallel hypersurfaces
• Mean curvature flow in higher codimension
• Mean curvature flow in submanifolds