Results 11 to 20 of about 38 (38)
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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Isometry Lie algebras of indefinite homogeneous spaces of finite volume
Proceedings of the London Mathematical Society, Volume 119, Issue 4, Page 1115-1148, October 2019., 2019 Abstract Let g be a real finite‐dimensional Lie algebra equipped with a symmetric bilinear form ⟨·,·⟩. We assume that ⟨·,·⟩ is nil‐invariant. This means that every nilpotent operator in the smallest algebraic Lie subalgebra of endomorphisms containing the adjoint representation of g is an infinitesimal isometry for ⟨·,·⟩.
Oliver Baues +2 more
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Hausdorff measure of the singular set of quasiregular maps on Carnot groups
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 35, Page 2203-2220, 2003., 2003 Recently, the theory of quasiregular mappings on Carnot groups has been developed intensively. Let ν stand for the homogeneous dimension of a Carnot group and let m be the index of the last vector space of the corresponding Lie algebra. We prove that the (ν − m − 1)‐dimensional Hausdorff measure of the image of the branch set of a quasiregular mapping ...
Irina Markina
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C1,α-rectifiability in low codimension in Heisenberg groups
Analysis and Geometry in Metric SpacesA natural higher-order notion of C1,α{C}^{1,\alpha }-rectifiability ...
Idu Kennedy Obinna +1 more
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On the heat kernel of the Rumin complex and Calderón reproducing formula
Analysis and Geometry in Metric SpacesWe derive several properties of the heat equation with the Hodge operator associated with the Rumin’s complex on Heisenberg groups and prove several properties of the fundamental solution.
Ciatti Paolo +2 more
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Advanced Nonlinear StudiesOn general Carnot groups, the definition of a possible hypoelliptic Hodge-Laplacian on forms using the Rumin complex has been considered in (M. Rumin, “Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie ...
Baldi Annalisa, Tripaldi Francesca
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Polynomial and horizontally polynomial functions on Lie groups. [PDF]
Ann Mat Pura Appl, 2022 Antonelli G, Le Donne E.
europepmc +1 more source
Counting function estimates for coherent frames and Riesz sequences. [PDF]
Ann Mat Pura ApplPapageorgiou E, van Velthoven JT.
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$L^p$\ multipliers on the Heisenberg group.
Michigan Mathematical Journal, 1979Giancarlo Mauceri
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Hilbert transforms along curves, II: A flat case
Duke Mathematical Journal, 1985Michael Christ
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