Maximal tubular surfaces of arbitrary codimension in the Minkowski space

A surface, given by a $C^2$-immersion $u\colon M\to R_1^{n+1}$, is said to be tubular if the cross-sections $u(M)\cap\Pi$ are compact for all hyperplanes $\Pi$ that are orthogonal to the time axis. Space-like surfaces with zero mean curvature vector are maximal. The extrinsic properties of maximal tubular surfaces are studied in this paper. In particular, it is proved that if such a surface, of dimension $p\geqslant 3$, has a singularity, then it has finite spread along the time axis.