General curvature estimates for stable H-surfaces in 3-manifolds and applications

Details General curvature estimates for stable H-surfaces in 3-manifolds and applications General curvature estimates for stable H-surfaces in 3-manifolds and applications

2009-02-20

arxiv.org/abs/0902.3572v2

Mathematics

Differential Geometry

22 pages

Scientific paper

We obtain an estimate for the norm of the second fundamental form of stable H-surfaces in Riemannian 3-manifolds with bounded sectional curvature. Our estimate depends on the distance to the boundary of the surface and on the bounds on the geometry of the ambient manifold but not on the manifold itself. We give some applications, in particular we obtain an interior gradient estimate for H-sections in Killing submersions.

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