Published Paper
Inserted: 5 apr 2023
Last Updated: 22 apr 2024
Journal: Advanced Nonlinear Studies
Volume: 24
Number: 1
Pages: 44-73
Year: 2024
Doi: 101515/ans-2023-0115
Abstract:
We classify hypersurfaces with rotational symmetry and positive constant $r$-th mean curvature in $\mathbb H^n \times \mathbb R$. 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 $\mathbb H^n \times \mathbb R$: we show that compact connected hypersurfaces of constant $r$-th mean curvature embedded in $\mathbb H^n \times [0,\infty)$ with boundary in the slice $\mathbb H^n \times \{0\}$ are topological disks under suitable assumptions.