Minimal surfaces on Riemannian manifolds (Q1262555)

The aim of this paper is to find disk-type minimal surfaces spanning a given boundary \(\Gamma\) in a Riemannian manifold. In \(S^ n\) for each Jordan curve there are at least two solutions of the problem. Further information is contained in the following theorem of \textit{S.-T. Yau} [Semin. differential geometry, Ann. Math. Stud. 102, 3-71 (1982; Zbl 0478.53001)] for which the present author announces to have a proof. Suppose that a compact manifold N admits no minimal sphere; if there are two strictly stable minimal disks bounded by the Jordan curve \(\Gamma\), then there exists an unstable minimal surface bounded by \(\Gamma\). The author also establishes a minimax principle for the energy functional in order to estimate the number of minimal surfaces. No proofs are given.