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

摘要

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