Minimal hypersurfaces in ℝⁿ×S^m

Abstract

We classify minimal hypersurfaces in R n × S m , n, m ≥ 2, which are invariant by the canonical action of O(n) × O(m). We also construct compact and noncompact examples of invariant hypersurfaces of constant mean curvature. We show that the minimal hypersurfaces and the noncompact constant mean curvature hypersurfaces are all unstable.