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- W4300534479 abstract "For constant mean curvature surfaces of class $C^2$ immersed inside Sasakian sub-Riemannian 3-manifolds we obtain a formula for the second derivative of the area which involves horizontal analytical terms, the Webster scalar curvature of the ambient manifold, and the extrinsic shape of the surface. Then we prove classification results for complete surfaces with empty singular set which are stable, i.e., second order minima of the area under a volume constraint, inside the 3-dimensional sub-Riemannian space forms. In the first Heisenberg group we show that such a surface is a vertical plane. In the sub-Riemannian hyperbolic 3-space we give an upper bound for the mean curvature of such surfaces, and we characterize the horocylinders as the only ones with squared mean curvature 1. Finally we deduce that any complete surface with empty singular set in the sub-Riemannian 3-sphere is unstable." @default.
- W4300534479 created "2022-10-03" @default.
- W4300534479 creator A5008012446 @default.
- W4300534479 date "2010-07-15" @default.
- W4300534479 modified "2023-09-24" @default.
- W4300534479 title "Complete stable CMC surfaces with empty singular set in Sasakian sub-Riemannian 3-manifolds" @default.
- W4300534479 doi "https://doi.org/10.48550/arxiv.1007.2597" @default.
- W4300534479 hasPublicationYear "2010" @default.
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