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

2009/02/20 by Harold Rosenberg, Rosenberg, Harold, Rabah Souam +3 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.0902.3572

22 pages

arxiv created 2009/06/24 · arxiv updated 2009/12/01

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 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.

Cited by

• Stable Bernstein Problem in certain positively curved manifolds

Related

• A note on area estimates for stable H-hypersurfaces and applications
• On stable constant mean curvature surfaces in S2 X R and H2 X R
• Radius estimates for nearly stable H-hypersurfaces of dimension 2, 3, and 4
• On the first stability eigenvalue of constant mean curvature surfaces into homogeneous 3-manifolds
• Optimal length estimates for stable CMC surfaces in 3-space forms