Mean curvature flow of graphs in generalized Robertson-Walker spacetimes with perpendicular Neumann boundary condition

被引：0

作者：

de Lira, Jorge H. S. ^{[1
]}

Roing, Fernanda ^{[1
]}

机构：

[1] Univ Fed Ceara, Dept Matemat, BR-60455900 Fortaleza, Ceara, Brazil

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2023年 / 202卷 / 02期

关键词：

Mean curvature flow; Generalized Robertson-Walker spacetimes; Constant mean curvature hypersurfaces; SPACELIKE HYPERSURFACES; UNIQUENESS;

D O I：

10.1007/s10231-022-01266-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the longtime existence for the mean curvature flow problem with a perpendicular Neumann boundary condition in a generalized Robertson-Walker (GRW) spacetime that obeys the null convergence condition. In addition, we prove that the metric of such a solution is conformal to the one of the leaf of the GRW in asymptotic time. Furthermore, if the initial hypersurface is mean convex, then the evolving hypersurfaces remain mean convex during the flow.

引用

页码：939 / 966

页数：28

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