Surfaces of annulus type with constant mean curvature in Lorentz-Minkowski space

Details Surfaces of annulus type with constant mean curvature in Lorentz-Minkowski space Surfaces of annulus type with constant mean curvature in Lorentz-Minkowski space

2005-01-12

arxiv.org/abs/math/0501188v1

Mathematics

Differential Geometry

19 pages, 4 figures

Scientific paper

In this paper we solve the Plateau problem for spacelike surfaces with constant mean curvature in Lorentz-Minkowski three-space $\l^3$ and spanning two circular (axially symmetric) contours in parallel planes. We prove that rotational symmetric surfaces are the only compact spacelike surfaces in $\l^3$ of constant mean curvature bounded by two concentric circles in parallel planes. As conclusion, we characterize spacelike surfaces of revolution with constant mean curvature as the only that either i) are the solutions of the exterior Dirichlet problem for constant boundary data or ii) have an isolated conical-type singularity.

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