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REGULARITY OF SOAP FILM-LIKE SURFACES SPANNING GRAPHS IN A RIEMANNIAN MANIFOLD
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 Title & Authors
REGULARITY OF SOAP FILM-LIKE SURFACES SPANNING GRAPHS IN A RIEMANNIAN MANIFOLD
Gulliver, Robert; Park, Sung-Ho; Pyo, Jun-Cheol; Seo, Keom-Kyo;
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 Abstract
Let M be an n-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant . Using the cone total curvature TC() of a graph which was introduced by Gulliver and Yamada [8], we prove that the density at any point of a soap film-like surface spanning a graph is less than or equal to . From this density estimate we obtain the regularity theorems for soap film-like surfaces spanning graphs with small total curvature. In particular, when n
 Keywords
soap film-like surface;graph;density;
 Language
English
 Cited by
 References
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