Calculus of Variations and Geometric Measure Theory

F. Maggi - A. Scardicchio - S. Stuvard

Soap films with gravity and almost-minimal surfaces

created by stuvard on 13 Jul 2018
modified on 27 Jun 2019


Published Paper

Inserted: 13 jul 2018
Last Updated: 27 jun 2019

Journal: Discrete Cont. Dyn. Syst.
Year: 2019
Doi: 10.3934/dcds.2019236

ArXiv: 1807.05200 PDF
Links: Webpage


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