Source: Osaka J. Math. Volume 46, Number 1
(2009), 1-20.
In this paper we consider a free boundary problem for spacelike
surfaces in the 3-dimensional Lorentz-Minkowski space $\mathbb{L}^{3}$
whose energy functional involves the area of a surface and
a timelike potential. The critical points of this energy for
any volume-preserving admissible variation are spacelike surfaces
supported in a plane and whose mean curvature is a linear
function of the time coordinate. In this paper, we consider
those surfaces that are invariant in a parallel coordinate
to the support plane. We call these surfaces stationary bands.
We establish existence of such surfaces and we investigate
their qualitative properties. Finally, we give estimates of
its size in terms of the initial data.
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