数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (1): 171-186.doi: 10.1016/S0252-9602(12)60203-3

• 论文 • 上一篇    下一篇

SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

吴加勇   

  1. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
  • 收稿日期:2011-09-19 出版日期:2013-01-20 发布日期:2013-01-20
  • 基金资助:

    This work is partially supported by the NSFC (11101267, 11271132), the Innovation Program of Shanghai Municipal Education Commission (13YZ087), and the Science and Technology Program of Shanghai Maritime University (20120061).

SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

 WU Jia-Yong   

  1. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
  • Received:2011-09-19 Online:2013-01-20 Published:2013-01-20
  • Supported by:

    This work is partially supported by the NSFC (11101267, 11271132), the Innovation Program of Shanghai Municipal Education Commission (13YZ087), and the Science and Technology Program of Shanghai Maritime University (20120061).

摘要:

Given a family of smooth immersions of closed hypersurfaces in a locally sym-metric Riemannian manifold with bounded geometry, moving by mean curvature flow, we show that at the first finite singular time of mean curvature flow, certain subcritical quan-tities concerning the second fundamental form blow up. This result not only generalizes a result of Le-Sesum and Xu-Ye-Zhao, but also extends the latest work of Le in the Euclidean case.

关键词: mean curvature flow, Riemannian submanifold, integral curvature, maximal existence time

Abstract:

Given a family of smooth immersions of closed hypersurfaces in a locally sym-metric Riemannian manifold with bounded geometry, moving by mean curvature flow, we show that at the first finite singular time of mean curvature flow, certain subcritical quan-tities concerning the second fundamental form blow up. This result not only generalizes a result of Le-Sesum and Xu-Ye-Zhao, but also extends the latest work of Le in the Euclidean case.

Key words: mean curvature flow, Riemannian submanifold, integral curvature, maximal existence time

中图分类号: 

  • 53C40