Stable minimal submanifolds in compact rank one symmetric spaces (Q1076990)

\textit{H. B. Lawson} jun. and \textit{J. Simons} [Ann. Math., II. Ser. 98, 427-450 (1973; Zbl 0283.53049)] classified stable minimal submanifolds and stable currents on \(S^ n\) and \(P^ n({\mathbb{C}})\). In this paper we complete the classification of stable minimal submanifolds in compact rank one symmetric spaces (i.e. \(S^ n\), \(P^ n({\mathbb{R}})\), \(P^ n({\mathbb{C}})\), \(P^ n({\mathbb{H}})\) and \(P^ 2(Cay))\). Our results are generalized to rectifiable currents. Furthermore we discuss the instability of rectifiable currents on compact convex hypersurfaces and some rank two symmetric spaces.