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Analysis and Geometry in Metric Spaces, 2018 Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance.
Le Donne Enrico
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Analysis and Geometry in Metric Spaces, 2014 We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity.
Freeman David M.
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A Cornucopia of Carnot Groups in Low Dimensions
Analysis and Geometry in Metric Spaces, 2022 Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating.
Le Donne Enrico, Tripaldi Francesca
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On rectifiable measures in Carnot groups: representation. [PDF]
Calc Var Partial Differ Equ, 2022 AbstractThis paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of $$\mathscr {P}$$ P -rectifiable measure. First, we show that in arbitrary Carnot groups the natural infinitesimal definition of rectifiabile measure, i.e., the definition given in ...
Antonelli G, Merlo A.
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On Rectifiable Measures in Carnot Groups: Existence of Density. [PDF]
J Geom Anal, 2022 AbstractIn this paper, we start a detailed study of a new notion of rectifiability in Carnot groups: we say that a Radon measure is$${\mathscr {P}}_h$$Ph-rectifiable, for$$h\in {\mathbb {N}}$$h∈N, if it has positiveh-lower density and finiteh-upper density almost everywhere, and, at almost every point, it admits a unique tangent measure up to multiples.
Antonelli G, Merlo A.
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On the ∞-Laplacian on Carnot Groups
Journal of Mathematical Sciences, 2022 We prove Lipschitz estimates for viscosity solutions to Poisson problem for the infinity Laplacian in general Carnot groups.
Fausto Ferrari +2 more
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Rearrangements in Carnot Groups [PDF]
Acta Mathematica Sinica, English Series, 2019 In this paper we extend the notion of rearrangement of nonnegative functions to the setting of Carnot groups. We define rearrangement with respect to a given family of anisotropic balls B_r or equivalently with respect to a gauge |x|, and prove basic regularity properties of this construction.
Manfredi, Juan J. +1 more
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Notions of Convexity in Carnot Groups [PDF]
Communications in Analysis and Geometry, 2003 The aim of this interesting paper is to study appropriate notions of convexity in the setting of Carnot groups \(G\). First, the notion of strong \(H\)-convexity is examined. Some arguments showing that the concept is to restrictive are presented. Then the notion of weakly \(H\)-convex functions is defined.
DANIELLI D. +2 more
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