Calculus of Variations and Geometric Measure Theory

A. Pinamonti - G. Stefani - S. Verzellesi

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

created by verzellesi on 22 Dec 2023
modified on 25 Jun 2024


Submitted Paper

Inserted: 22 dec 2023
Last Updated: 25 jun 2024

Year: 2023


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.