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2013•Communications in Analysis and GeometryOpen access

Mean curvature flow of higher codimension in hyperbolic spaces

Kefeng Liu, Hongwei Xu, Fei Ye, Entao Zhao

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Abstract

In this paper, we investigate the convergence for the mean curvature flow of closed submanifolds with arbitrary codimension in space forms.Particularly, we prove that the mean curvature flow deforms a closed submanifold satisfying a pinching condition in a hyperbolic space form to a round point in finite time.

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What this paper is about

In this paper, we investigate the convergence for the mean curvature flow of closed submanifolds with arbitrary codimension in space forms.Particularly, we prove that the mean curvature flow deforms a closed submanifold satisfying a pinching condition in a hyperbolic space form to a round point in finite time.

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OpenAlex reports 23 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we investigate the convergence for the mean curvature flow of closed submanifolds with arbitrary codimension in space forms.Particularly, we prove that the mean curvature flow deforms a closed submanifold satisfying a pinching condition in a hyperbolic space form to a round point in finite time.

Key concepts: Mathematics, Codimension, Mean curvature flow, Pure mathematics, Curvature, Flow (mathematics), Geometric flow, Mathematical analysis

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