#### Vol. 305, No. 2, 2020

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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
##### Authors
 Rafael López Departamento de Geometría y Topología Universidad de Granada Granada Spain