Results 11 to 20 of about 18,321 (180)
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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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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Rearrangements in Carnot Groups [PDF]
Acta Mathematica Sinica, English Series, 2019 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.
Manfredi, Juan J. +1 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.
DANIELLI D. +2 more
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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 ...
Antonelli, Gioacchino, Merlo, Andrea
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Structure of porous sets in Carnot groups [PDF]
Illinois Journal of Mathematics, 2017 We show that any Carnot group contains a closed nowhere dense set which has measure zero but is not $σ$-porous with respect to the Carnot-Carathéodory (CC) distance. In the first Heisenberg group we observe that there exist sets which are porous with respect to the CC distance but not the Euclidean distance and vice-versa.
Pinamonti A., Speight G.
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The Traveling Salesman Theorem in Carnot groups [PDF]
Calculus of Variations and Partial Differential Equations, 2018 Let $\mathbb{G}$ be any Carnot group. We prove that, if a subset of $\mathbb{G}$ is contained in a rectifiable curve, then it satisfies Peter Jones' geometric lemma with some natural modifications. We thus prove one direction of the Traveling Salesman Theorem in $\mathbb{G}$.
Chousionis, Vasilis +2 more
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Nonexistence Results for Semilinear Equations in Carnot Groups
Analysis and Geometry in Metric Spaces, 2013 In this paper, following [3], we provide some nonexistence results for semilinear equations in the the class of Carnot groups of type ★.This class, see [20], contains, in particular, all groups of step 2; like the Heisenberg group, and also Carnot ...
Ferrari Fausto, Pinamonti Andrea
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Pliability, or the whitney extension theorem for curves in carnot groups [PDF]
, 2016 The Whitney extension theorem is a classical result in analysis giving a necessary and sufficient condition for a function defined on a closed set to be extendable to the whole space with a given class of regularity.
Juillet, Nicolas, Sigalotti, Mario
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Laser-induced thermoelectric effects in electrically biased nanoscale constrictions
Nanophotonics, 2018 Electrically biased metal nanostructures are at the core of innovative multifunctional integrated devices that control the flow of electrons and photons at the nanoscale.
Mennemanteuil Marie-Maxime +6 more
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