Abstract
Let S be a smooth compact imbedded surface in ℝ3 and let B be the unit disc in ℝ2. We consider the problem of finding a surface that minimizes area among all surfaces which have the topological type of a disc and which have boundaries in a given nontrivial homotopy class H of curves γ: ∂B → S. We show that H can be decomposed into finitely many homotopy classes H1, …, Hk for which the problem is solvable.
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