Semigenerated Carnot algebras and applications to sub-Riemannian perimeter

DOI10.1007/s00209-021-02744-4OpenAlexW3160900022WikidataQ109744194 ScholiaQ109744194MaRDI QIDQ2664680

Terhi Moisala, Enrico Le Donne

Publication date: 17 November 2021

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.08619

zbMATH Keywords

Carnot algebraLie wedgesemigroup generatedconstant intrinsic normalEngel-type algebrasfinite sub-Riemannian perimeterhorizontal half-spacetipe diamondtrimmed algebra

Mathematics Subject Classification ID

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) General properties and structure of real Lie groups (22E15) Structure of topological semigroups (22A15) Sub-Riemannian geometry (53C17)

Related Items

On rectifiable measures in Carnot groups: existence of density, On rectifiable measures in Carnot groups: representation, Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups, Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2, Marstrand-Mattila rectifiability criterion for 1-codimensional measures in Carnot groups, Nowhere differentiable intrinsic Lipschitz graphs

Cites Work

• Regularity of sets with constant horizontal normal in the Engel group
• Regularity of sets with constant intrinsic normal in a class of Carnot groups
• Differentiating maps into \(L^1\), and the geometry of BV functions
• Lie semigroups and their applications
• On the structure of finite perimeter sets in step 2 Carnot groups
• A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries
• Control theory from the geometric viewpoint.
• Sets with constant normal in Carnot groups: properties and examples
• Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane
• BV functions and sets of finite perimeter in sub-Riemannian manifolds
• A Basis for Free Lie Rings and Higher Commutators in Free Groups
• Rectifiability and perimeter in the Heisenberg group