The perpendicular Neumann problem for mean curvature flow with a timelike cone boundary condition. (English) Zbl 1296.53131

Summary: 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 space-like. Using a blowdown argument, we show that under renormalisation this flow converges towards a homothetically expanding hyperbolic solution.


53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
35K59 Quasilinear parabolic equations
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