Iury Domingos

Overdetermined equations and support functions on the hyperbolic and de Sitter planes

We study overdetermined equations on the hyperbolic and de Sitter planes by means of the support-function representation of zero mean curvature surfaces in Lorentz--Minkowski three-space. On the hyperbolic plane, solutions of $\Delta u-2u=0$ give rise to branched spacelike maximal surfaces. We prove that, on a bounded...