Geodesic
Extrinsic dimensions of tubular minimal hypersurfaces
Sbornik. Mathematics, Tome 59 (1988) no. 1, pp. 237-245

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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. 
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     title = {Extrinsic dimensions of tubular minimal hypersurfaces},
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A. D. Vedenyapin; V. M. Miklyukov. Extrinsic dimensions of tubular minimal hypersurfaces. Sbornik. Mathematics, Tome 59 (1988) no. 1, pp. 237-245. http://geodesic.mathdoc.fr/item/SM_1988_59_1_a12/