Contents Online
Mathematical Research Letters
Volume 4 (1997)
Number 5
The structure of stable minimal hypersurfaces in $I\!\!R^{n+1}$
Pages: 637 – 644
DOI: https://dx.doi.org/10.4310/MRL.1997.v4.n5.a2
Authors
Abstract
We provide a new topological obstruction for complete stable minimal hypersurfaces in $I\!\!R^{n+1}$. For $n\geq 3$, we prove that a complete orientable stable minimal hypersurface in $I\!\!R^{n+1}$ cannot have more than one end by showing the existence of a bounded harmonic function based on the Sobolev inequality for minimal submanifolds \cite{MS} and by applying the Liouville theorem for harmonic functions due to Schoen-Yau \cite{SY}.
Published 1 January 1997