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On constant higher order mean curvature hypersurfaces in $\mathbb H^n \times \mathbb R$
- Publication Year :
- 2023
-
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.<br />Comment: 30 pages, 3 tables, 14 figures. Figures 9-14 added, minor changes in the exposition. Accepted for publication in Advanced Nonlinear Studies
- Subjects :
- Mathematics - Differential Geometry
53C42, 53A10
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2304.00349
- Document Type :
- Working Paper