论文标题
垂直于Neumann边界条件的广义Robertson-Walker空间中图的平均曲率流动
Mean curvature flow of graphs in Generalized Robertson-Walker spacetimes with perpendicular Neumann boundary condition
论文作者
论文摘要
我们证明，在遵守无效收敛条件下的广义罗伯逊·沃克（GRW）时期，垂直的诺伊曼边界条件的平均曲率流问题的长期存在。此外，我们证明了这种溶液的度量与渐近时间的GRW叶片之一相吻合。此外，如果初始超表面是平均凸，则在流动过程中，不断发展的超曲面仍然是平均凸。
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.
