THE MEAN CURVATURE FLOW BY PARALLEL HYPERSURFACES

被引：6

作者：

Santos dos Reis, Hiuri Fellipe ^{[1
]}

Tenenblat, Keti ^{[1
]}

机构：

[1] Univ Brasilia, Dept Math, BR-70910900 Brasilia, DF, Brazil

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 11期

关键词：

Isoparametric hypersurface; mean curvature flow; parallel hypersurface; space forms; ISOPARAMETRIC HYPERSURFACES; PRINCIPAL CURVATURES;

D O I：

10.1090/proc/14178

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown that a hypersurface of a space form is the initial data for a solution to the mean curvature flow by parallel hypersurfaces if and only if it is isoparametric. By solving an ordinary differential equation, explicit solutions are given for all isoparametric hypersurfaces of space forms. In particular, for such hypersurfaces of the sphere, the exact collapsing time into a focal submanifold is given in terms of its dimension, the principal curvatures, and their multiplicities.

引用

页码：4867 / 4878

页数：12

共 50 条

[21] SOLITON SOLUTIONS OF THE MEAN CURVATURE FLOW AND MINIMAL HYPERSURFACES
Hungerbuehler, Norbert
Mettler, Thomas
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (06) : 2117 - 2126
[22] Mean curvature flow with free boundary on smooth hypersurfaces
Buckland, JA
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2005, 586 : 71 - 90
[23] On the mean curvature type flow for convex capillary hypersurfaces in the ball
Yingxiang Hu
Yong Wei
Bo Yang
Tailong Zhou
[J]. Calculus of Variations and Partial Differential Equations, 2023, 62
[24] On the mean curvature type flow for convex capillary hypersurfaces in the ball
Hu, Yingxiang
Wei, Yong
Yang, Bo
Zhou, Tailong
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2023, 62 (07)
[25] Weak solutions of inverse mean curvature flow for hypersurfaces with boundary
Marquardt, Thomas
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2017, 728 : 237 - 261
[26] On an extension of the Hk mean curvature flow of closed convex hypersurfaces
Li, Yi
[J]. GEOMETRIAE DEDICATA, 2014, 172 (01) : 147 - 154
[27] Mean curvature flow with surgeries of two-convex hypersurfaces
Huisken, Gerhard
Sinestrari, Carlo
[J]. INVENTIONES MATHEMATICAE, 2009, 175 (01) : 137 - 221
[28] The avoidance principle for noncompact hypersurfaces moving by mean curvature flow
White, Brian
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2024, 63 (05)
[29] Stability of hypersurfaces with constant mean curvature trapped between two parallel hyperplanes
Koiso, Miyuki
Miyamoto, Umpei
[J]. JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2024, 41 (01) : 233 - 268
[30] Stability of hypersurfaces of constant mean curvature with free boundary in two parallel hyperplanes
Koiso, Miyuki
Miyamoto, Umpei
[J]. JSIAM LETTERS, 2023, 15 : 9 - 12

← 1 2 3 4 5 →