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Coincidence set of minimal surfaces for the thin obstacle

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Abstract

We consider the Thin Obstacle Problem for minimal surfaces in two dimensions. The coincidence set for an analytic obstacle is proved to be a finite union of intervals. We show also that the topological structure of the coincidence set is generically identical to the above in the space of twice-continuously differentiable obstacles.

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  1. Department of Mathematics, University of Kentucky, 40502, Lexington, KY, USA

    Ioannis Athanasopoulos

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  1. Ioannis Athanasopoulos
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Athanasopoulos, I. Coincidence set of minimal surfaces for the thin obstacle. Manuscripta Math 42, 199–209 (1983). https://doi.org/10.1007/BF01169583

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  • DOI: https://doi.org/10.1007/BF01169583

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