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We study immersed critical points X of an elliptic parametric functional F(X) = ? BF(Xu ? Xv)dudv that are spanned into a partially free boundary configuration {G,S} in R3. We suppose that S is a cylindrical support surface and that G is a closed Jordan arc with a simple convex projection. Under geometrically reasonable assumptions on {G,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.

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