A partial solution of the isoperimetric problem for the Heisenberg group

2006/01/17 by N. Garofalo, Nicola Garofalo, Donatella Danielli +6
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Spectral Theory in Mathematical Physics #advanced mathematical theories #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.math/0601412

32 pages, 1 figure

openalex publication_date 2006/01/17 · arxiv created 2006/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a partial solution to the isoperimetric problem in the Heisenberg group.

Citations

• Metric Structures for Riemannian and Non-Riemannian Spaces
• Minimal Surfaces in the Heisenberg Group
• An integral formula for total gradient variation
• Constant mean curvature surfaces in sub-Riemannian geometry

Related

• Stability of Heisenberg Isoperimetric Profiles
• Convex isoperimetric sets in the Heisenberg group
• Hypergeometric solutions of the closed eigenvalue problem on Heisenberg Isoperimetric Profiles
• Sharp geometric rigidity of isometries on Heisenberg group
• Isoperimetric domains in homogeneous three-manifolds and the isoperimetric constant of the Heisenberg group H¹