Journal of Differential Geometry

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

Harold Rosenberg, Rabah Souam, and Eric Toubiana

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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.

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J. Differential Geom., Volume 84, Number 3 (2010), 623-648.

First available in Project Euclid: 14 July 2010

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Rosenberg, Harold; Souam, Rabah; Toubiana, Eric. General curvature estimates for stable H-surfaces in 3-manifolds applications. J. Differential Geom. 84 (2010), no. 3, 623--648. doi:10.4310/jdg/1279114303.

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