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- Title
Soap films with gravity and almost-minimal surfaces.
- Authors
Maggi, Francesco; Stuvard, Salvatore; Scardicchio, Antonello
- 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.
- Subjects
MINIMAL surfaces; SOAP; GRAVITY; CURVATURE
- Publication
Discrete & Continuous Dynamical Systems: Series A, 2019, Vol 39, Issue 12, p6877
- ISSN
1078-0947
- Publication type
Article
- DOI
10.3934/dcds.2019236