Lipschitz approximation of almost \mathbb G-perimeter minimizing boundaries in plentiful groups

2023/12/24 by Andrea Pinamonti, Giorgio Stefani, Pinamonti, Andrea +3
Mathematics · #28A75 #35R03 #49Q05 #53C17 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2312.15473

openalex publication_date 2023/12/24 · openalex created_date 2023/12/29 · openalex updated_date 2026/07/30

Abstract

We prove that the boundary of an almost minimizer of the intrinsic perimeter in a plentiful group can be approximated by intrinsic Lipschitz graphs. Plentiful groups are Carnot groups of step~2 whose center of the Lie algebra is generated by any co-dimension one horizontal subspace. For example, H-type groups not isomorphic to the first Heisenberg group are plentiful. Our results provide the first extension of the regularity theory of intrinsic minimal surfaces beyond the family of Heisenberg groups.

Related

• Plateau's Problem for intrinsic graphs in the Heisenberg Group
• Examples of area-minimizing surfaces in the subriemannian Heisenberg group H¹ with low regularity
• A notable family of entire intrinsic minimal graphs in the Heisenberg group which are not perimeter minimizing
• Area-minimizing horizontal graphs with low-regularity in the sub-Finsler Heisenberg group ℍ¹
• Regularity of non-characteristic minimal graphs in the Heisenberg group H¹