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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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.

Article information

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

Dates
First available in Project Euclid: 14 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1279114303

Digital Object Identifier
doi:10.4310/jdg/1279114303

Mathematical Reviews number (MathSciNet)
MR2669367

Zentralblatt MATH identifier
1198.53062

Citation

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. https://projecteuclid.org/euclid.jdg/1279114303


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