On constant higher order mean curvature hypersurfaces in \mathbb Hⁿ × \mathbb R

2023/04/01 by Barbara Nelli, Nelli, Barbara, Giuseppe Pipoli +3
Mathematics · #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2304.00349

openalex publication_date 2023/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify hypersurfaces with rotational symmetry and positive constant r-th mean curvature in \mathbb Hⁿ × \mathbb R. Specific constant higher order mean curvature hypersurfaces invariant under hyperbolic translation are also treated. Some of these invariant hypersurfaces are employed as barriers to prove a Ros--Rosenberg type theorem in \mathbb Hⁿ × \mathbb R: we show that compact connected hypersurfaces of constant r-th mean curvature embedded in \mathbb Hⁿ × [0,∞) with boundary in the slice \mathbb Hⁿ × \0\ are topological disks under suitable assumptions.

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