Spacelike Hypersurfaces with Free Boundary in the Minkowski Space under the Effect of a Timelike Potential
نویسندگان
چکیده
In this paper we consider a variational problem for spacelike hypersurfaces in the (n + 1)-dimensional Lorentz-Minkowski space L, whose critical points are hypersurfaces supported in a spacelike hyperplane determined by two facts: the mean curvature is a linear function of the distance to and the hypersurface makes a constant angle with along its boundary. We prove that the hypersurface is rotational symmetric with respect to a straight-line orthogonal to and that each (non-empty) intersection with a parallel hyperplane to is a round (n − 1)-sphere. A similar result is proved for hypersurfaces trapped between two parallel hyperplanes.
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