Projectability and uniqueness of F-stable immersions with partially free boundaries

Abstract

We study immersed critical points X of an elliptic parametric functional Ᏺ(X) = B F(X u ∧ X v ) du dv that are spanned into a partially free boundary configuration { , } in ‫ޒ‬ 3 . We suppose that is a cylindrical support surface and that is a closed Jordan arc with a simple convex projection. Under geometrically reasonable assumptions on { , }, F, and X we prove the projectability and uniqueness of stable immersions. This generalizes a result for minimal surfaces obtained by Hildebrandt and Sauvigny.