Results 21 to 30 of about 12,319,056 (272)
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
Escape from compact sets of normal curves in Carnot groups [PDF]
E S A I M: Control, Optimisation and Calculus of Variations, 2023 In the setting of subFinsler Carnot groups, we consider curves that satisfy the normal equation coming from the Pontryagin Maximum Principle. We show that, unless it is constant, each such a curve leaves every compact set, quantitatively.
Enrico Le Donne, Nicola Paddeu
openalex +3 more sources
Sub-Riemannian calculus on hypersurfaces in Carnot groups [PDF]
, 2007 We develope basic geometric quantities and properties of hypersurfaces in Carnot ...
Donatella Danielli +2 more
openalex +6 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
Approximations of Sobolev norms in Carnot groups [PDF]
Communications in Contemporary Mathematics, 2010 This paper deals with a notion of Sobolev space $W^{1,p}$ introduced by J.Bourgain, H.Brezis and P.Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by A.Ponce to obtain a Poincar\'e-type
Adams R. +14 more
core +4 more sources
Yamabe-type equations on Carnot groups [PDF]
Potential Analysis, 2017 This article is concerned with a class of elliptic equations on Carnot groups depending of one real positive parameter and involving a critical nonlinearity.
Bisci, Giovanni Molica +1 more
core +6 more sources
The parabolic p-Laplace equation in Carnot groups [PDF]
, 2014 By employing a Carnot parabolic maximum principle, we show existence-uniqueness of viscosity solutions to a class of equations modeled on the parabolic infinite Laplace equation in Carnot groups.
Thomas Bieske, Erin Martin
openalex +4 more sources
Sharp Hardy Identities and Inequalities on Carnot Groups
Advanced Nonlinear Studies, 2021 In this paper we establish general weighted Hardy identities for several subelliptic settings including Hardy identities on the Heisenberg group, Carnot groups with respect to a homogeneous gauge and Carnot–Carathéodory metric, general nilpotent groups ...
Nguyen Lam
exaly +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
Ricci curvatures in Carnot groups [PDF]
arXiv, 2013 We study metric contraction properties for metric spaces associated with left-invariant sub-Riemannian metrics on Carnot groups. We show that ideal sub-Riemannian structures on Carnot groups satisfy such properties and give a lower bound of possible curvature exponents in terms of the datas.
arxiv +7 more sources