Accepted Paper

Inserted: 22 dec 2023
Last Updated: 22 jan 2025

Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Year: 2025

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.

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