O(m) � O(n)-Invariant Minimal Hypersurfaces in $\mathbb{R}$ m+n

Abstract

We classify the nonextendable immersed O(m) × O(n)-invariant minimal hypersurfaces in the Euclidean space \(\mathbb{R}\)m+n, m, n ≥ 3, analyzing also whether they are embedded or stable. We show also the existence of embedded, complete, stable minimal hypersurfaces in \(\mathbb{R}\)m+n, m + n ≥ 8, m, n ≥ 3 not homeomorphic to \(\mathbb{R}\)m+n−1 that are O(m) × O(n)-invariant.