Rigidity of area-minimizing hyperbolic surfaces in three-manifolds (Q363211)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Rigidity of area-minimizing hyperbolic surfaces in three-manifolds |
scientific article; zbMATH DE number 6203574
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rigidity of area-minimizing hyperbolic surfaces in three-manifolds |
scientific article; zbMATH DE number 6203574 |
Statements
Rigidity of area-minimizing hyperbolic surfaces in three-manifolds (English)
0 references
2 September 2013
0 references
Let \(M\) be a three-manifold with scalar curvature greater than or equal to \( -2\) and \(\Sigma \subset M\) an imbedded compact oriented Riemann surface of genus \(g(\Sigma)>1\), which is locally area-minimizing. The author proves that then the area of \(\Sigma\) is at least \(4\pi (g(\Sigma) - 1)\). In the equality case he proves that the induced metric on \(\Sigma\) has constant Gauss curvature equal to \(-1\). Some other related results are proved as well.
0 references
Riemann surface
0 references
area-minimizing
0 references
hyperbolic manifold
0 references
0 references
0 references
0 references
0 references
