Results 11 to 20 of about 12,322,898 (284)
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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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
doaj +5 more sources
Note on the $q$-Logarithmic Sobolev and $p$-Talagrand Inequalities on Carnot Groups [PDF]
, 2021 In the setting of Carnot groups, we prove the $q-$Logarithmic Sobolev inequality for probability measures as a function of the Carnot-Carath\'eodory distance. As an application, we use the Hamilton-Jacobi equation in the setting of Carnot groups to prove the $p-$Talagrand inequality and hypercontractivity.
Esther Bou Dagher
arxiv +3 more sources
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.
europepmc +5 more sources
Hardy, Rellich and Uncertainty principle inequalities on Carnot Groups [PDF]
arXiv, 2006 In this paper we prove sharp weighted Hardy-type inequalities on Carnot groups with the homogeneous norm $N=u^{1/(2-Q)}$ associated to Folland's fundamental solution $u$ for the sub-Laplacian $\Delta_{\mathbb{G}}$. We also prove uncertainty principle, Caffarelli-Kohn-Nirenberg and Rellich inequalities on Carnot groups.
İsmail Kömbe
arxiv +3 more sources
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
core +5 more sources
On coincidence of $p$-module of a family of curves and $p$-capacity on the Carnot group
, 2003 The notion of the extremal length and the module of families of curves has been studied extensively and has given rise to a lot of applications to complex analysis and the potential theory.
Irina Markina
openalex +3 more sources
BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups
Analysis and Geometry in Metric Spaces, 2015 Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is a ball of G, then there exists a subset Z ⊂ B, whose image in H under f has small Hausdorff content, such that B\Z can be decomposed into a controlled number of pieces, the ...
Li Sean
doaj +3 more sources
Review of Carnot Battery Technology Commercial Development
Energies, 2022 Carnot batteries are a quickly developing group of technologies for medium and long duration electricity storage. It covers a large range of concepts which share processes of a conversion of power to heat, thermal energy storage (i.e., storing thermal ...
Vaclav Novotny +3 more
doaj +2 more sources
Rigidity of quasiconformal maps on Carnot groups [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2013 We show that quasiconformal maps on many Carnot groups must be biLipschitz. In particular, this is the case for 2-step Carnot groups with reducible first layer. These results have implications for the rigidity of quasiisometries between negatively curved solvable Lie groups.
arxiv +5 more sources