Maximal tubes and bands in Minkowski space

Spacelike surfaces of zero mean curvature in Minkowski space are considered, and finite time conditions for the existence of tubes and bands of codimension 1 are given. For two-dimensional bands of arbitrary codimension, the bounds of admissible rate of exit to a hypersurface are indicated, and some information on the number of branchings is presented. A distinctive feature of the work is the use in estimates, as a basic characteristic of a surface, of the local time flow through sections of a tube or a band.