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

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 lea...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2023-04, Vol.202 (2), p.939-966
Main Authors: de Lira, Jorge H. S., Roing, Fernanda
Format: Article
Language:English
Subjects:
Boundary conditions
Curvature
Hyperspaces
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-022-01266-y