## B. Nelli - G. Pipoli - G. Russo

# On constant higher order mean curvature hypersurfaces in $\mathbb H^n \times \mathbb R$

created by russo on 05 Apr 2023

modified on 22 Apr 2024

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BibTeX]

*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

**Links:**
Link to journal

**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.