Generalized convexity and quantitative estimates for constant mean curvature spacelike hypersurfaces in Anti-de Sitter space

2025/08/07 by Trebeschi, Enrico
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.05349

Abstract

We study the principal curvatures of properly embedded constant mean curvature hypersurfaces in the Anti-de Sitter space ℍ^n,1. We generalize the notion of convex hull and give an upper bound on the principal curvatures which only depends on the width of the H-shifted convex hull. This analysis has two direct consequences. First, it allows to bound the sectional curvature of H-hypersurfaces by an explicit function of the the width of the H-shifted convex hull. Second, we bound the quasiconfromal dilatation of a class of quasiconformal maps on the hyperbolic plane ℍ², called θ-landslides, in terms of the cross-ratio norm of their quasi-symmetric extension on ∂_∞ℍ².

Citations

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Related

• Constant mean curvature hypersurfaces in Anti-de Sitter space
• Some sharp estimates for convex hypersurfaces of pinched normal\n curvature
• An Application of Maximum Principle to space-like Hypersurfaces with Constant Mean Curvature in Anti-de Sitter Space
• Convex hypersurfaces with pinched principal curvatures and flow of convex hypersurfaces by high powers of curvature
• On stable hypersurfaces with constant mean curvature in Euclidean spaces