The aim of this paper is to prove a uniqueness theorem for stable minimal surfaces X: B→R~3 of the type of the disk which are stationary in a boundary configuration <Γ, S> consisting of a surface S and of a Jordan arc Γ with end-points on S. The existence of such surfaces for a prescribed configuration <Γ, S> was established by Courant under fairly general assumptions on Γ and S, while H. Lewy proved the first basic results on boundary regularity of minimizers. A detailed investigation of this problem with regard to existence, boundary regularity and properties of the free trace can be found in the recent monograph [3]; cf. also [2] and [9].
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