Results 1 to 10 of about 14,219 (239)
On rectifiable measures in Carnot groups: representation. [PDF]
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]
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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Geometric inequalities in Carnot groups [PDF]
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
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A metric characterization of Carnot groups [PDF]
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
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Convex hull property and exclosure theorems for H-minimal hypersurfaces in carnot groups [PDF]
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
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Isodiametric inequality in Carnot groups
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
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Multicomplexes on Carnot Groups and Their Associated Spectral Sequence. [PDF]
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]
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
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A Cornucopia of Carnot Groups in Low Dimensions
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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A note on lifting of Carnot groups
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
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