On the Calabi-Yau problem for maximal surfaces in L^3

TL;DR

This paper constructs a weakly complete maximal surface in Lorentz-Minkowski space bounded by a hyperboloid, featuring exclusively lightlike singularities, advancing understanding of maximal surfaces in Lorentzian geometry.

Contribution

It provides the first example of a weakly complete maximal surface in L^3 bounded by a hyperboloid with lightlike singularities.

Findings

Constructed a weakly complete maximal surface in L^3

Surface is bounded by a hyperboloid

All singularities are of lightlike type

Abstract

In this paper we construct an example of a weakly complete maximal surface in the Lorentz-Minkowski space L^3, which is bounded by a hyperboloid. Moreover, all the singularities of our example are of lightlike type.