The extension of the Hk mean curvature flow in Riemannian manifolds

被引：0
作者：
Hongbing Qiu
Yunhua Ye
Anqiang Zhu
机构：
[1] Wuhan University,School of Mathematics and Statistics
来源：
Chinese Annals of Mathematics, Series B | 2014年 / 35卷
关键词：
mean curvature flow; Riemannian manifold; Sobolev type inequality; Moser iteration; 53C44; 53C21;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, the authors consider a family of smooth immersions Ft: Mn → Nn+1 of closed hypersurfaces in Riemannian manifold Nn+1 with bounded geometry, moving by the Hk mean curvature flow. The authors show that if the second fundamental form stays bounded from below, then the Hk mean curvature flow solution with finite total mean curvature on a finite time interval [0, Tmax) can be extended over Tmax. This result generalizes the extension theorems in the paper of Li (see “On an extension of the Hk mean curvature flow, Sci. China Math., 55, 2012, 99–118”).
引用
收藏
页码：191 / 208
页数：17
相关论文
共 17 条
  • [1] Han X(2010)On the extension of the mean curvature flow in arbitrary codimension Inter. J. Math. 21 1429-1438
  • [2] Sun J(1975)Sobolev and isoperimetric inequalities for Riemannian submanifolds Comm. Pure Appl. Math. 28 765-766
  • [3] Hoffman D(1984)Flow by mean curvature of convex surfaces into spheres J. Differential Geom. 20 237-266
  • [4] Spruck J(1986)Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature Invent. Math. 84 463-480
  • [5] Huisken G(2011)On the extension of the mean curvature flow Math. Z. 267 583-604
  • [6] Huisken G(2012)On an extension of the Sci. China Math. 55 99-118
  • [7] Le N Q(1973) mean curvature flow Comm. Pure Appl. Math. 26 361-379
  • [8] Sesum N(2005)Sobolev and mean-value inequalities on generalized submanifolds of ℝ Math. Z. 251 721-733
  • [9] Li Y(1997)Evolution of convex hypersurfaces by powers of the mean curvature New York J. Math. 3 103-118
  • [10] Michael G(2013)Harnack inequalities for curvature flows depending on mean curvature Acta Mathematica Scientia Ser. B 33 171-186
12