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

Abstract

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 bound on the sectional curvature but not on the manifold itself. We give some applications, in particular we obtain an interior gradient estimate for H-sections in Killing submersions. © 2010 Journal of Differential Geometry. © 2010 Applied Probability Trust.