Results 11 to 20 of about 18,179 (207)
A sufficient condition for nonrigidity of Carnot groups [PDF]
Mathematische Zeitschrift, 2018 In this article we consider contact mappings on Carnot groups. Namely, we are interested in those mappings whose differential preserves the horizontal space, defined by the first stratum of the natural stratification of the Lie algebra of a Carnot group.
Ottazzi, Alessandro
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A note on lifting of Carnot groups
Revista 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.
Andrea Bonfiglioli, Francesco Uguzzoni
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On rectifiable measures in Carnot groups: representation [PDF]
Calculus of Variations and Partial Differential Equations, 2021 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 ...
Gioacchino Antonelli, Andrea Merlo
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Rearrangements in Carnot Groups [PDF]
Acta Mathematica Sinica, English Series, 2018 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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Viscosity convex functions on Carnot groups [PDF]
Proceedings of the American Mathematical Society, 2003 We prove that any upper semicontinuous v-convex function in any Carnot group is h-convex.
Changyou Wang
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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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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.
Duy Minh Nhieu +3 more
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A Cornucopia of Carnot Groups in Low Dimensions
Analysis and Geometry in Metric Spaces, 2022 AbstractStratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating. When a stratified group is equipped with a left-invariant path distance that is homogeneous with respect to the automorphisms induced by the derivation, this metric space is known as Carnot ...
Le Donne, Enrico, Tripaldi, Francesca
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Invertible Carnot Groups [PDF]
Analysis and Geometry in Metric Spaces, 2014 Abstract 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.
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Conformal maps of Carnot groups
Annales Academiae Scientiarum Fennicae Mathematica, 2015 If f is a conformal mapping defined on a connected open subset of a Carnot group G, then either f is the composition of a translation, a dilation and an isometry, or G is the nilpotent Iwasawa component of a real rank 1 simple Lie group S, and f arises from the action of S on G, viewed as an open subset of S/P, where P is a parabolic subgroup of G and ...
Cowling, MG, Ottazzi, A
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