On the compactness of hypersurfaces with finite total curvature via mean curvature flow

被引：0

作者：

Cao, Shunjuan ^{[1
,2
]}

Zhao, Entao ^{[3
]}

机构：

[1] Zhejiang Agr & Forestry Univ, Dept Math, Linan 311300, Peoples R China

[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China

[3] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Peoples R China

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2020年 / 158卷

基金：

中国国家自然科学基金;

关键词：

Hypersurfaces; Mean curvature flow; Compactness; Finite total curvature; RICCI CURVATURE; RIEMANNIAN-MANIFOLDS; SUBMANIFOLDS; THEOREMS;

D O I：

10.1016/j.geomphys.2020.103857

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a complete hypersurface in the Euclidean space, we assume that the second fundamental form is bounded and the mean curvature is bounded from below by a positive constant. We prove that if the L-p-norm of the trace-free second fundamental form for some p >= 2 is finite, then the hypersurface is compact. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：8

共 28 条

[1] A THEOREM OF MYERS [J].

AMBROSE, W .

DUKE MATHEMATICAL JOURNAL, 1957, 24 (03) :345-348

[2]

[Anonymous], 2006, GRADUATE STUDIES MAT

[3] Complete hypersurfaces with constant mean curvature and finite total curvature [J].

Berard, P ;

Do Carmo, M ;

Santos, W .

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 1998, 16 (03) :273-290

[4]

Berard P., 1999, MAT CONT, V17, P77

[5]

Brendle S., 2009, Geometry, Analysis, and Algebraic Geometry: Forty Years of the Journal of Differential Geometry, Volume13 of Survey in Differential Geometry, VXIII, P49

[6] ON RICCI CURVATURE AND GEODESICS [J].

CALABI, E .

DUKE MATHEMATICAL JOURNAL, 1967, 34 (04) :667-&

[7]

Chen BL, 2007, COMMUN ANAL GEOM, V15, P435

[8] Complete Riemannian manifolds with pointwise pinched curvature [J].

Chen, BL ;

Zhu, XP .

INVENTIONES MATHEMATICAE, 2000, 140 (02) :423-452

[9] Smoothing Riemannian metrics with Ricci curvature bounds [J].

Dai, XZ ;

Wei, GF ;

Ye, RG .

MANUSCRIPTA MATHEMATICA, 1996, 90 (01) :49-61

[10]

do Carmo M, 2019, COMMUN ANAL GEOM, V27, P1251

← 1 2 3 →