Codimension two surfaces pinched by normal curvature evolving by mean curvature flow

被引：7

作者：

Baker, Charles ^{[1
]}

Huy The Nguyen ^{[2
]}

机构：

[1] CSIRO, Hlth & Biosecur, Australian E Hlth Res Ctr, RBWH, Level 5 UQ Hlth Sci Bldg 901-16, Herston, Qld 4029, Australia

[2] Queen Mary Univ London, Sch Math Sci, Mile End Rd, London E1 4NS, England

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2017年 / 34卷 / 06期

关键词：

Curvature flow; Mean curvature; Nonlinear parabolic equations; SUBMANIFOLDS; SPHERES;

D O I：

10.1016/j.anihpc.2016.10.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that codimension two surfaces satisfying a nonlinear curvature condition depending on normal curvature smoothly evolve by mean curvature flow to round points. Crown Copyright (C) 2016 Published by Elsevier Masson SAS. All rights reserved.

引用

页码：1599 / 1610

页数：12

共 50 条

[31] Level set approach to mean curvature flow in arbitrary codimension
Ambrosio, L
Soner, HM
JOURNAL OF DIFFERENTIAL GEOMETRY, 1996, 43 (04) : 693 - 737
[32] Self-shrinkers for the mean curvature flow in arbitrary codimension
Claudio Arezzo
Jun Sun
Mathematische Zeitschrift, 2013, 274 : 993 - 1027
[33] Self-shrinkers of the mean curvature flow in arbitrary codimension
Smoczyk, K
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2005, 2005 (48) : 2983 - 3004
[34] MEAN CURVATURE FLOW OF COMPACT SPACELIKE SUBMANIFOLDS IN HIGHER CODIMENSION
Guilfoyle, Brendan
Klingenberg, Wilhelm
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 372 (09) : 6263 - 6281
[35] Self-shrinkers for the mean curvature flow in arbitrary codimension
Arezzo, Claudio
Sun, Jun
MATHEMATISCHE ZEITSCHRIFT, 2013, 274 (3-4) : 993 - 1027
[36] Mean Curvature Flow of Arbitrary Codimension in Complex Projective Spaces
Li Lei
Hongwei Xu
Chinese Annals of Mathematics, Series B, 2023, 44 : 857 - 892
[37] A Canonical Neighborhood Theorem for Mean Curvature Flow in Higher Codimension
Naff, Keaton
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (13) : 11499 - 11536
[38] Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery
Langford, Mat
Huy The Nguyen
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (06)
[39] Mean curvature flow singularities for mean convex surfaces
Gerhard Huisken
Carlo Sinestrari
Calculus of Variations and Partial Differential Equations, 1999, 8 : 1 - 14
[40] Mean curvature flow singularities for mean convex surfaces
Huisken, G
Sinestrari, C
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1999, 8 (01) : 1 - 14

← 1 2 3 4 5 →