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arXiv · 1807.05200

Soap films with gravity and almost-minimal surfaces

Francesco Maggi·Antonello Scardicchio·Salvatore Stuvard
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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.

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Francesco Maggi, Antonello Scardicchio, Salvatore Stuvard. 2018-07-13. Soap films with gravity and almost-minimal surfaces. https://doi.org/10.3934/dcds.2019236

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