Spacelike surfaces with free boundary in the Lorentz-Minkowski space

TL;DR

This paper studies spacelike surfaces with constant mean curvature and free boundary conditions in Lorentz-Minkowski space, classifying solutions when the support surface is a pseudosphere and extending the analysis to higher dimensions.

Contribution

It characterizes spacelike surfaces with free boundary and constant mean curvature in Lorentz-Minkowski space, especially when the support surface is a pseudosphere, and extends results to higher dimensions.

Findings

Surfaces are either planar discs or hyperbolic caps when support is a pseudosphere.

Provides classification results for spacelike surfaces with free boundary in Lorentz-Minkowski space.

Extends the analysis to higher-dimensional Lorentz-Minkowski spaces.

Abstract

We investigate a variational problem in the Lorentz-Minkowski space $\l^3$ 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 $\l^{n+1}$.