Spacelike surfaces with free boundary in the Lorentz-Minkowski space

We investigate a variational problem in the Lorentz-Minkowski space $ł^3$ whose critical points are spacelike surfaces with constant mean curvature and making constant contact angle with a given support surface along its common boundary. We show that if the support surface is a pseudosphere, then the surface is a planar disc or a hyperbolic cap. We also study the problem of spacelike hypersurfaces with free boundary in the higher dimensional Lorentz-Minkowski space $ł^{n+1}$.

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