Sets with constant normal in Carnot groups: properties and examples

DOI10.4171/CMH/510zbMath1475.53033arXiv1910.12117OpenAlexW3136113887WikidataQ109931526 ScholiaQ109931526MaRDI QIDQ2030902

Costante Bellettini, Enrico Le Donne

Publication date: 8 June 2021

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.12117

zbMATH Keywords

cone propertyLie wedgeCarnot-Lebesgue representativeconstant horizontal normalfree Carnot groupintrinsic Lipschitz graphintrinsic rectifiable setmonotone directionsemigroup generatedsubriemannian perimeter measure

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Nilpotent and solvable Lie groups (22E25) Calibrations and calibrated geometries (53C38) Sub-Riemannian geometry (53C17)

Related Items

Metric equivalences of Heintze groups and applications to classifications in low dimension, A rectifiability result for finite-perimeter sets in Carnot groups, Semigenerated Carnot algebras and applications to sub-Riemannian perimeter, Intrinsic rectifiability via flat cones in the Heisenberg group, Unextendable Intrinsic Lipschitz Curves:, Horizontally affine functions on step-2 Carnot algebras, Monotone sets and local minimizers for the perimeter in Carnot groups, Precisely monotone sets in step-2 rank-3 Carnot algebras, Polynomial and horizontally polynomial functions on Lie groups

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