Geodesic
On the bore radius for minimal surfaces
Matematičeskie zametki, Tome 59 (1996) no. 6, pp. 909-913

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A least upper bound for the inner radius $R$ of an opening in a complete minimal hypersurface contained in a parallel layer is given. Namely, if $\Delta$ is the width of this layer, then $R\le\Delta/(2c_p)$, where $c_p$ is an absolute constant depending only on the dimension $p$ of the minimal hypersurface. 
@article{MZM_1996_59_6_a9,
     author = {V. G. Tkachev},
     title = {On the bore radius for minimal surfaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {909--913},
     publisher = {mathdoc},
     volume = {59},
     number = {6},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_6_a9/}
}
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V. G. Tkachev. On the bore radius for minimal surfaces. Matematičeskie zametki, Tome 59 (1996) no. 6, pp. 909-913. http://geodesic.mathdoc.fr/item/MZM_1996_59_6_a9/