Given any Γ=γ(S^1)⊂R^2, image of a Lipschitz curve γ:S^1→R^2, not necessarily injective, we provide an explicit formula for computing the value of (Formula presented.) where the infimum is computed among all Lipschitz maps u:B_1(0)→R^2 having boundary datum γ. This coincides with the area of a minimal disk spanning Γ, i.e., a solution of the Plateau problem of disk type. The novelty of the results relies in the fact that we do not assume the curve γ to be injective and our formula allows arbitrary self-intersections.
On the singular planar Plateau problem
Caroccia Marco;
2024-01-01
Abstract
Given any Γ=γ(S^1)⊂R^2, image of a Lipschitz curve γ:S^1→R^2, not necessarily injective, we provide an explicit formula for computing the value of (Formula presented.) where the infimum is computed among all Lipschitz maps u:B_1(0)→R^2 having boundary datum γ. This coincides with the area of a minimal disk spanning Γ, i.e., a solution of the Plateau problem of disk type. The novelty of the results relies in the fact that we do not assume the curve γ to be injective and our formula allows arbitrary self-intersections.File in questo prodotto:
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