Area density and regularity for soap film-like surfaces spanning graphs

@inproceedings{Gulliver2006AreaDA,
  title={Area density and regularity for soap film-like surfaces spanning graphs},
  author={Robert Gulliver and Sumio Yamada},
  year={2006}
}
For a boundary configuration Γ consisting of arcs and vertices, with two or more arcs meeting at each vertex, we treat the problem o f estimating the area density of a soap film-like surface Σ spanningΓ. Σ is assumed to be strongly stationary for area with respect to Γ. We introduce a notion of total curvature Ctot(Γ) for suchgraphs, or nets,Γ. When the ambient manifold M has nonpositive sectional curvatures, we show that 2π times the area density of Σ at any point is less than or equal to Ctot… CONTINUE READING

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