Stationary bands in three-dimensional Minkowski space

Abstract

In this paper we consider a free boundary problem in the 3-dimensional Lorentz-Minkowski space $\l^3$ which deals spacelike surfaces whose mean curvature is a linear function of the time coordinate and the boundary moves in a given support plane. We study spacelike surfaces that project one-to-one into a strip of the support and that locally are critical points of a certain energy functional involving the area of the surface, a timelike potential and preserves the volume enclosed by the surface. 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.