Extrinsic dimensions of tubular minimal hypersurfaces

It is established that every embedded minimal hypersurface in $R^{n+1}$ that is tubular with respect to some line has a bounded projection on that line for $n\geqslant3$. An estimate of the length of the projection is given, and it is shown that equality in this estimate can be attained only on a catenoid.
Bibliography: 12 titles.