Results 41 to 50 of about 12,258,354 (255)
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.
openaire +3 more sources
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
openaire +4 more sources
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
openaire +5 more sources
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
doaj +1 more source
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.
openaire +3 more sources
A sufficient condition for nonrigidity of Carnot groups [PDF]
Mathematische Zeitschrift, 2007 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.
Alessandro Ottazzi, Alessandro Ottazzi
openaire +4 more sources
Geometric inequalities in Carnot groups [PDF]
Pacific Journal of Mathematics, 2013 Let $\GG$ be a sub-Riemannian $k$-step Carnot group of homogeneous dimension $Q$. In this paper, we shall prove several geometric inequalities concerning smooth hypersurfaces (i.e. codimension one submanifolds) immersed in $\GG$, endowed with the $\HH$-perimeter measure.
openaire +3 more sources
Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation
Bruno Pini Mathematical Analysis Seminar, 2020 We study the interior regularity of weak solutions to subelliptic quasilinear PDEs in Carnot groups of the formΣi=1m1Xi (Φ(|∇Hu|2)Xiu) = 0. Here ∇Hu = (X1u,...,Xmiu) is the horizontal gradient, δ > 0 and the exponent p ∈ [2, p*), where p* depends on ...
András Domokos, Juan J. Manfredi
doaj +1 more source
A reverse coarea-type inequality in Carnot groups
Annales de l'Institut Fourier, 2022 . We prove a coarea-type inequality for a continuously Pansu differentiable function acting between two Carnot groups endowed with homogeneous distances. We assume that the level sets of the function are uniformly lower Ahlfors regular and that the Pansu ...
Francesca Corni
semanticscholar +1 more source
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
doaj +1 more source