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On rectifiable measures in Carnot groups: representation. [PDF]

open access: hybridCalc 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.
europepmc   +8 more sources

Invertible Carnot Groups [PDF]

open access: yesAnalysis 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.
doaj   +3 more sources

Geometric inequalities in Carnot groups [PDF]

open access: yesPacific Journal of Mathematics, 2012
Let $\GG$ be a sub-Riemannian $k$-step Carnot group of homogeneous dimension $Q$. In this paper, we shall prove several geometric inequalities concerning smooth hypersurfaces (i.e.
Montefalcone, Francescopaolo
core   +4 more sources

A metric characterization of Carnot groups [PDF]

open access: yesProceedings of the American Mathematical Society, 2014
We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are isometrically ...
Donne, Enrico Le
core   +3 more sources

Convex hull property and exclosure theorems for H-minimal hypersurfaces in carnot groups [PDF]

open access: yesAnalysis and Geometry in Metric Spaces, 2016
In this paper, we generalize to sub-Riemannian Carnot groups some classical results in the theory of minimal submanifolds. Our main results are for step 2 Carnot groups.
MONTEFALCONE, FRANCESCOPAOLO
core   +3 more sources

Isodiametric inequality in Carnot groups

open access: yesAnnales Academiae Scientiarum Fennicae Mathematica, 2010
The classical isodiametric inequality in the Euclidean space says that balls maximize the volume among all sets with a given diameter. We consider in this paper the case of Carnot groups.
Rigot, Severine
core   +6 more sources

Multicomplexes on Carnot Groups and Their Associated Spectral Sequence. [PDF]

open access: yesJ Geom Anal, 2023
AbstractThe aim of this paper is to give a thorough insight into the relationship between the Rumin complex on Carnot groups and the spectral sequence obtained from the filtration on forms by homogeneous weights that computes the de Rham cohomology of the underlying group.
Lerario A, Tripaldi F.
europepmc   +5 more sources

Rearrangements in Carnot Groups [PDF]

open access: greenActa 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.
Juan J. Manfredi   +1 more
openaire   +5 more sources

A Cornucopia of Carnot Groups in Low Dimensions

open access: yesAnalysis 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
doaj   +5 more sources

A note on lifting of Carnot groups

open access: bronzeRevista Matemática Iberoamericana, 2005
We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.
BONFIGLIOLI, ANDREA, UGUZZONI, FRANCESCO
openaire   +7 more sources

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