Soap films with gravity and almost-minimal surfaces
Analysis of PDEs
2019-10-03 v2 Mathematical Physics
Differential Geometry
math.MP
Optimization and Control
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
Cite
@article{arxiv.1807.05200,
title = {Soap films with gravity and almost-minimal surfaces},
author = {Francesco Maggi and Antonello Scardicchio and Salvatore Stuvard},
journal= {arXiv preprint arXiv:1807.05200},
year = {2019}
}
Comments
34 pages, 6 figures. Version 2: more detailed description of the proof of the estimates in Section 5 added