Exclusion of boundary branch points for minimal surfaces
Abstract In the present paper we prove two different theorems to exclude boundary branch points for minimal surfaces X in ℝn. The statements roughly read as follows: A minimal surface X has no branch points on the boundary ∂Ω, (1) if for any P ∈ X(∂Ω) there exists some strictly two-convex C2-subdomain U = U (P) ⊂ ℝn whose boundary ∂U contains P and such that X(–Ω) ⊂ –U; (2) or if for each point P ∈ X(∂Ω) there exists some strictly two-convex C2-subdomain U = U (P) ⊂ ℝn with P ∈ ∂U, X(∂Ω) ⊂ –U and such that ℝn ∖ U can be foliated by the boundaries of a family of strictly two-convex C2-subdomains of ℝn; (3) and in particular if X maps ∂Ω into the boundary of some strictly two-convex, star-shaped C2-subdomain of ℝn.