On the Calabi–Yau problem for maximal surfaces in L3L3

In this paper we construct an example of a maximal surface in the Lorentz–Minkowski space L3L3, which is bounded by a hyperboloid and weakly complete in the sense explained by Umehara and Yamada [M. Umehara, K. Yamada, Maximal surfaces with singularities in Minkowski space, Hokkaido Math. J. 35 (2006) 13–40].