arXiv:1611.02095 Abstract | arXiv Analytics

arXiv:1611.02095 [math.DG]Abstract References Reviews Resources

Quantitative stability for hypersurfaces with almost constant mean curvature in the hyperbolic space

Published 2016-11-07Version 1

We provide sharp stability estimates for the Alexandrov Soap Bubble Theorem in the hyperbolic space. The closeness to a single sphere is quantified in terms of the dimension, the measure of the hypersurface and the radius of the touching ball condition. As consequence we obtain a new pinching result for hypersurfaces in the hyperbolic space. Our approach is based on the method of moving planes. In this context we carefully review the method and we provide the first quantitative study in the hyperbolic space.

Categories: math.DG, math.AP

Subjects: 53C20, 53C21, 35B50, 53C24

Keywords: hyperbolic space, constant mean curvature, quantitative stability, hypersurface, sharp stability estimates

Related articles: Most relevant | Search more

arXiv:math/9810157 [math.DG] (Published 1998-10-28)

Moebius geometry of surfaces of constant mean curvature 1 in hyperbolic space

Udo Hertrich-Jeromin, Emilio Musso, Lorenzo Nicolodi

arXiv:0806.4666 [math.DG] (Published 2008-06-29)

On the index of constant mean curvature 1 surfaces in hyperbolic space

Levi Lopes de Lima, Wayne Rossman

arXiv:0803.2244 [math.DG] (Published 2008-03-14, updated 2009-05-05)

Vertical Ends of Constant Mean Curvature H=1/2 in H^2\times R