The perpendicular Neumann problem for mean curvature flow with a timelike cone boundary condition

Lambert, Ben

doi:10.1090/S0002-9947-2014-05865-0

The perpendicular Neumann problem for mean curvature flow with a timelike cone boundary condition
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Trans. Amer. Math. Soc. 366 (2014), 3373-3388 Request permission

Abstract:

This paper demonstrates existence for all time of mean curvature flow in Minkowski space with a perpendicular Neumann boundary condition, where the boundary manifold is a convex cone and the flowing manifold is initially spacelike. Using a blowdown argument, we show that under renormalisation this flow converges towards a homothetically expanding hyperbolic solution.

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