The structure of stable minimal hypersurfaces in IR
نویسندگان
چکیده
We provide a new topological obstruction for complete stable minimal hypersurfaces in IRn+1. For n ≥ 3, we prove that a complete orientable stable minimal hypersurface in IRn+1 cannot have more than one end by showing the existence of a bounded harmonic function based on the Sobolev inequality for minimal submanifolds [MS] and by applying the Liouville theorem for harmonic functions due to Schoen-Yau [SY].
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تاریخ انتشار 1997