Exclusion of boundary branch points for minimal surfaces
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Matthias Bergner
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-convexC2-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.
© by Oldenbourg Wissenschaftsverlag, Duisburg, Germany
Artikel in diesem Heft
- A Brunn–Minkowski inequality for a Finsler–Laplacian
- Irrationality of certain infinite series II
- Elastic catenoids
- On the distribution of zeros of monic polynomials with a given uniform norm on a quasidisk
- Universal approximation by translates of fundamental solutions of elliptic equations
- Exclusion of boundary branch points for minimal surfaces
- On the uniform convergence of double sine integrals over –ℝ 2+
Artikel in diesem Heft
- A Brunn–Minkowski inequality for a Finsler–Laplacian
- Irrationality of certain infinite series II
- Elastic catenoids
- On the distribution of zeros of monic polynomials with a given uniform norm on a quasidisk
- Universal approximation by translates of fundamental solutions of elliptic equations
- Exclusion of boundary branch points for minimal surfaces
- On the uniform convergence of double sine integrals over –ℝ 2+
