Spacelike surfaces with free boundary in the Lorentz-Minkowski space

Abstract

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

16 pages. Accepted in Classical and Quantum Gravity

References in corpus (1)

• Einstein equations in the null quasi-spherical gauge III: numerical algorithms