Exclusion of boundary branch points for minimal surfaces

摘要

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