Contracting pinched hypersurfaces in spheres by their mean curvature

Yan Li; Hongwei Xu; Entao Zhao

doi:10.4310/PAMQ.2015.v11.n2.a8

Contracting pinched hypersurfaces in spheres by their mean curvature

Yan Li
, Hongwei Xu
, Entao Zhao

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we study an open problem proposed in [10]. We prove that the mean curvature flow of hypersurfaces in the sphere will contract to a round point in finite time if the initial hypersurface satisfies a curvature pinching condition. Our theorem is a partial improvement of the convergence theorem due to Huisken [7].

Original language	English
Pages (from-to)	329-368
Number of pages	40
Journal	Pure and Applied Mathematics Quarterly
Volume	11
Issue number	2
DOIs	https://doi.org/10.4310/PAMQ.2015.v11.n2.a8
Publication status	Published - 2015
Externally published	Yes

Keywords

Curvature pinching
Hypersurface
Mean curvature flow
Sphere

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10.4310/PAMQ.2015.v11.n2.a8

Cite this

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title = "Contracting pinched hypersurfaces in spheres by their mean curvature",

abstract = "In this paper, we study an open problem proposed in [10]. We prove that the mean curvature flow of hypersurfaces in the sphere will contract to a round point in finite time if the initial hypersurface satisfies a curvature pinching condition. Our theorem is a partial improvement of the convergence theorem due to Huisken [7].",

keywords = "Curvature pinching, Hypersurface, Mean curvature flow, Sphere",

author = "Yan Li and Hongwei Xu and Entao Zhao",

year = "2015",

doi = "10.4310/PAMQ.2015.v11.n2.a8",

language = "English",

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T1 - Contracting pinched hypersurfaces in spheres by their mean curvature

AU - Li, Yan

AU - Xu, Hongwei

AU - Zhao, Entao

PY - 2015

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AB - In this paper, we study an open problem proposed in [10]. We prove that the mean curvature flow of hypersurfaces in the sphere will contract to a round point in finite time if the initial hypersurface satisfies a curvature pinching condition. Our theorem is a partial improvement of the convergence theorem due to Huisken [7].

KW - Curvature pinching

KW - Hypersurface

KW - Mean curvature flow

KW - Sphere

UR - https://www.scopus.com/pages/publications/84983382219

U2 - 10.4310/PAMQ.2015.v11.n2.a8

DO - 10.4310/PAMQ.2015.v11.n2.a8

M3 - Article

AN - SCOPUS:84983382219

SN - 1558-8599

VL - 11

SP - 329

EP - 368

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

IS - 2

ER -

Contracting pinched hypersurfaces in spheres by their mean curvature

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Keywords

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