Stability of Heisenberg Isoperimetric Profiles

2011/10/04 by Francescopaolo Montefalcone, Montefalcone, Francescopaolo
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #math.DG #math.MG

paper · pdf · doi:10.48550/arxiv.1110.0707

29 pages

openalex publication_date 2011/10/04 · arxiv created 2011/11/17 · arxiv updated 2011/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the context of sub-Riemannian Heisenberg groups Hn, n ≥ 1, we shall study Isoperimetric Profiles, which are closed compact hypersurfaces having constant horizontal mean curvature, very similar to ellipsoids. Our main goal is to study the stability of Isoperimetric Profiles.

Related

• Hypergeometric solutions of the closed eigenvalue problem on Heisenberg Isoperimetric Profiles
• A partial solution of the isoperimetric problem for the Heisenberg group
• Convex isoperimetric sets in the Heisenberg group
• Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group Hⁿ
• Curvature estimates for minimal hypersurfaces in the Heisenberg group