Results 41 to 50 of about 12,282,130 (266)
Heat and entropy flows in Carnot groups [PDF]
Revista Matemática Iberoamericana, 2019 We prove the correspondence between the solutions of the sub-elliptic heat equation in a Carnot group \mathbb G and the gradient flows of the relative entropy functional in the Wasserstein space of probability measures on \mathbb G ...
Ambrosio L., Stefani G.
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Exceptional families of measures on Carnot groups
Analysis and Geometry in Metric Spaces, 2023 AbstractWe study the families of measures on Carnot groups that have vanishingpp-module, which we callMp{M}_{p}-exceptional families. We found necessary and sufficient Conditions for the family of intrinsic Lipschitz surfaces passing through a common point to beMp{M}_{p}-exceptional forp≥1p\ge 1.
Franchi, Bruno, Markina, Irina
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Conformal and CR mappings on Carnot groups [PDF]
Proceedings of the American Mathematical Society, Series B, 2020 We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove that on products of such groups, all CR and anti-CR maps are product maps, up to a permutation isomorphism, and ...
Cowling, MG, Li, J, Ottazzi, A, Wu, Q
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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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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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A metric characterization of Carnot groups [PDF]
Proceedings of the American Mathematical Society, 2014 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.
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Analysis and Geometry in Metric Spaces, 2014 A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra.We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups.
Franchi Bruno +2 more
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Quasisymmetric maps of boundaries of amenable hyperbolic groups [PDF]
, 2014 In this paper we show that if $Y=N \times \mathbb{Q}_m$ is a metric space where $N$ is a Carnot group endowed with the Carnot-Caratheodory metric then any quasisymmetric map of $Y$ is actually bilipschitz. The key observation is that $Y$ is the parabolic
Dymarz, Tullia
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Monge's transport problem in the Heisenberg group [PDF]
, 2010 We prove the existence of solutions to Monge transport problem between two compactly supported Borel probability measures in the Heisenberg group equipped with its Carnot-Caratheodory distance assuming that the initial measure is absolutely continuous ...
Ambrosio B. +15 more
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Subelliptic and parametric equations on Carnot groups [PDF]
Proceedings of the American Mathematical Society, 2015 This article concerns a class of elliptic equations on Carnot groups depending on one real parameter. Our approach is based on variational methods. More precisely, we establish the existence of at least two weak solutions for the treated problem by using a direct consequence of the celebrated Pucci-Serrin theorem and of a local minimum result for ...
Molica Bisci G, Ferrara M
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