Published Paper
Inserted: 13 jul 2018
Last Updated: 27 jun 2019
Journal: Discrete Cont. Dyn. Syst.
Year: 2019
Doi: 10.3934/dcds.2019236
Abstract:
Motivated by the study of the equilibrium equations for a soap film hanging from a wire frame, we prove a compactness theorem for surfaces with asymptotically vanishing mean curvature and fixed or converging boundaries. In particular, we obtain sufficient geometric conditions for the minimal surfaces spanned by a given boundary to represent all the possible limits of sequences of almost-minimal surfaces. Finally, we provide some sharp quantitative estimates on the distance of an almost-minimal surface from its limit minimal surface.
Keywords: minimal surfaces, Plateau problem, integral currents, capillarity, Integral varifolds
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