Analytic extension of Jorge-Meeks type maximal surfaces in Lorentz-Minkowski 3-space

The Jorge-Meeks $n$-noid ($n\ge 2$) is a complete minimal surface of genus zero with $n$ catenoidal ends in the Euclidean 3-space ${\mathit{R}}^3$, which has $(2\pi \mathrm{/}n)$-rotation symmetry with respect to its axis. In this paper, we show that the corresponding maximal surface $f_n$ in Lorentz-Minkowski 3-space ${\mathit{R}}_1^3$ has an analytic extension ${\tilde{f}}_n$ as a properly embedded zero mean curvature surface. The extension changes type into a time-like (minimal) surface.