Minimal submanifolds with sublinear height growth must have Euclidean volume growth, implying an optimal Bernstein theorem for stable hypersurfaces in any dimension.
Osserman, Global properties of minimal surfaces in E^3 and E^n , Ann
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Minimal submanifolds confined in space
Minimal submanifolds with sublinear height growth must have Euclidean volume growth, implying an optimal Bernstein theorem for stable hypersurfaces in any dimension.