MEAN CURVATURE FLOW OF GRAPHS IN WARPED PRODUCTS

被引：5

作者：

Borisenko, Alexander A. ^{[1
]}

Miquel, Vicente ^{[2
]}

机构：

[1] Kharkov Natl Univ, Fac Math, Geometry Dept, UA-61077 Kharkov, Ukraine

[2] Univ Valencia, Dept Geometria & Topol, E-46100 Burjassot, Valencia, Spain

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 364卷 / 09期

关键词：

Differential geometry; algebraic geometry; RIEMANNIAN-MANIFOLDS; HYPERBOLIC SPACE; HYPERSURFACES; EVOLUTION;

D O I：

10.1090/S0002-9947-2012-05425-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be a complete Riemannian manifold which is either compact or has a pole, and let phi be a positive smooth function on M. In the warped product M x R-phi, we study the flow by the mean curvature of a locally Lipschitz continuous graph on M and prove that the flow exists for all time and that the evolving hypersurface is C-infinity for t > 0 and is a graph for all t. Moreover, under certain conditions, the flow has a well-defined limit.

引用

页码：4551 / 4587

页数：37

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