Complete minimal spheres and projective planes in \(R^ n\) with simple ends (Q1106488)

Suppose M is a complete 2-dimensional Riemannian manifold of finite total curvature and let x: \(M\to R^ n\) be an isometric minimal immersion. In case M is a sphere or projective plane with two simple ends a list of the possible immersions is given. For example, up to similarity, there are exactly two such projective planes in \(R^ 4\). Applications to the question of the existence of complete unoriented area-minimizing surfaces are discussed.