We classify hypersurfaces with rotational symmetry and positive constant r-th mean curvature in ℍn × 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 ℍn × ℝ: we show that compact connected hypersurfaces of constant r-th mean curvature embedded in ℍn × [0, ∞) with boundary in the slice ℍn × {0} are topological disks under suitable assumptions.

On constant higher order mean curvature hypersurfaces in ℍn × ℝ

Nelli B.
;
Pipoli G.;
2024-01-01

Abstract

We classify hypersurfaces with rotational symmetry and positive constant r-th mean curvature in ℍn × 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 ℍn × ℝ: we show that compact connected hypersurfaces of constant r-th mean curvature embedded in ℍn × [0, ∞) with boundary in the slice ℍn × {0} are topological disks under suitable assumptions.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/231620
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact