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

2016/11/07 by Ciraolo, Giulio, Vezzoni, Luigi
#35B50 #53C20 #53C21 (Primary) #53C24 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.02095

Abstract

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.

Related

• Quantitative stability for hypersurfaces with almost constant curvature in space forms
• Quantitative estimates for almost constant mean curvature hypersurfaces
• On the stability for Alexandrov's Soap Bubble theorem
• A sharp quantitative version of Alexandrov's theorem via the method of moving planes
• Optimal quantitative stability estimates for Alexandrov's Soap Bubble Theorem via Gagliardo-Nirenberg-type interpolation inequalities