Evolution of hypersurfaces by powers of mean curvature minus an external force field

doi:10.1007/s11464-012-0218-1

Front Math Chin

2012, Vol. 7

Issue (4) : 717-723 https://doi.org/10.1007/s11464-012-0218-1

RESEARCH ARTICLE

Evolution of hypersurfaces by powers of mean curvature minus an external force field

Yannan LIU(

)

Department of Mathematics, Beijing Technology and Business University, Beijing 100048, China

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Abstract

In this paper, we study the evolution of hypersurfaces by powers of mean curvature minus an external force field. We prove that when the power is 2, the flow has a long-time smooth solution for all time under some conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the external force field, with its any order derivatives, is bounded, and the field is convex with its eigenvalues satisfying a pinch inequality.

Keywords Parabolic equation mean curvature flow maximum principle (for tensor)

Corresponding Author(s): LIU Yannan,Email:liuyn@th.btbu.edu.cn

Issue Date: 01 August 2012

Cite this article:

Yannan LIU. Evolution of hypersurfaces by powers of mean curvature minus an external force field[J]. Front Math Chin, 2012, 7(4): 717-723.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-012-0218-1
https://academic.hep.com.cn/fmc/EN/Y2012/V7/I4/717

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