The two-dimensional analogue of the Lorentzian catenary and the Dirichlet problem

Abstract

In this paper we generalize in Lorentz-Minkowski space $\l^3$ the two-dimensional analogue of the catenary of Euclidean space. We solve the Dirichlet problem for bounded mean convex domains and spacelike boundary data that have a spacelike extension to the domain. We also classify all singular maximal surfaces of $\l^3$ invariant by a uniparametric group of translations and rotations.