Evolution of noncompact hypersurfaces by mean curvature minus a kind of external force field

Yannan Liu

doi:10.1007/s11464-010-0004-x

Front. Math. China ›› 2010, Vol. 5 ›› Issue (2) : 311 -317. DOI: 10.1007/s11464-010-0004-x

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Evolution of noncompact hypersurfaces by mean curvature minus a kind of external force field

Yannan Liu ¹^,^a

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Abstract

In this paper, we study the evolution of a noncompact hypersurface moving by mean curvature minus an external force field. We prove that the flow has a long-time smooth solution for a kind of special external force fields if the initial hypersurface is a Lipschitz entire graph with linear growth.

Keywords

parabolic equation / mean curvature flow / maximum principle

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Yannan Liu. Evolution of noncompact hypersurfaces by mean curvature minus a kind of external force field. Front. Math. China, 2010, 5(2): 311-317 DOI:10.1007/s11464-010-0004-x

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