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

Rafael López

Vol. 305 (2020), No. 2, 693–719

DOI: 10.2140/pjm.2020.305.693

Abstract

We generalize in Lorentz–Minkowski space ${\mathbb{𝕃}}^3$ the two-dimensional analogue of the catenary of Euclidean space. We solve the Dirichlet problem when the bounded domain is mean convex and the boundary data has a spacelike extension to the domain. We also classify all singular maximal surfaces of ${\mathbb{𝕃}}^3$ invariant by a uniparametric group of translations and rotations.

Keywords

singular maximal surface, Dirichlet problem, invariant surface

Mathematical Subject Classification 2010

Primary: 53A10, 53C42

Milestones

Received: 15 February 2019

Accepted: 4 December 2019

Published: 29 April 2020