Results 1 to 10 of about 14,667 (220)
A Cornucopia of Carnot Groups in Low Dimensions [PDF]
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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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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Convex Hull Property and Exclosure Theorems for H-Minimal Hypersurfaces in Carnot Groups [PDF]
Analysis 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
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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 the ∞-Laplacian on Carnot Groups [PDF]
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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Coercive Inequalities on Carnot Groups: Taming Singularities [PDF]
Analysis and Mathematical Physics, 2021 AbstractIn the setting of Carnot groups, we propose an approach of taming singularities to get coercive inequalities. To this end, we develop a technique to introduce natural singularities in the energy function U in order to force one of the coercivity conditions.
Esther Bou Dagher +1 more
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On the H.-Q. Li inequality on step-two Carnot groups [PDF]
Comptes Rendus. Mathématique, 2023 In this note we show that the gradient estimate of the heat semigroup, or more precisely the H.-Q. Li inequality, is preserved under tensorization, some suitable group epimorphism, and central sum. We also establish the Riemannian counterpart of the H.-Q.
Zhang, Ye
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Stability theorems for H-type Carnot groups [PDF]
The Journal of Geometric Analysis, 2022 We introduce the H-type deviation $δ({\mathbb G})$ of a step two Carnot group ${\mathbb G}$, which measures the deviation of the group from the class of Heisenberg-type groups. We show that $δ({\mathbb G})=0$ if and only if ${\mathbb G}$ carries a vertical metric which endows it with the structure of an H-type group. We compute the H-type deviation for
Jeremy T. Tyson
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The parabolic p-Laplace equation in Carnot groups [PDF]
, 2014 By employing a Carnot parabolic maximum principle, we show existence-uniqueness of viscosity solutions to a class of equations modeled on the parabolic infinite Laplace equation in Carnot groups.
Thomas Bieske, Erin Martin
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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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