2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152280We provide a new topological obstruction for complete stable minimal hypersurfaces in R^n. For $n\geq 4$, we prove that any complete orientable stable hypersurfaces in R^n has only one end. This follows from a more general analytic theorem we prove in the paper.LaTex Form, to appear in Math Research LettersDifferential Geometry53C21, 53C42text