Results 1 to 10 of about 2,300 (225)
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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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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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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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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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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Multicomplexes on Carnot Groups and Their Associated Spectral Sequence. [PDF]
J 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.
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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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Ball-Milling Assisted Iron-Catalyzed Difluoromethylation Toward the Synthesis of Valuable Oxindoles. [PDF]
ChemSusChemAn iron‐catalyzed difluoroalkylation of acrylamides under ball‐milling conditions affords oxindoles in up to 85% yield. Analytical studies reveal that the apparent piezoelectric activity originates from iron leaching caused by milling assembly abrasion during the reaction process. The iron‐catalyzed process proves to be efficient with a broad substrate
Solomin V +4 more
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A metric characterization of Carnot groups [PDF]
Proceedings of the American Mathematical Society, 2013 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 homogeneous.
Enrico Le Donne
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