Horizontally Affine Functions on Step-2 Carnot Algebras. [PDF]
J Geom Anal, 2023 Le Donne E, Morbidelli D, Rigot S.
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Reverse Poincare inequalities, Isoperimetry, and Riesz transforms in Carnot groups [PDF]
arXiv, 2015 We prove an optimal reverse Poincar\'e inequality for the heat semigroup generated by the sub-Laplacian on a Carnot group of any step. As an application we give new proofs of the isoperimetric inequality and of the boundedness of the Riesz transform in Carnot groups.
arxiv
A note on the engulfing property and the $\Gamma ^{1+ \alpha }$-regularity of convex functions in Carnot groups [PDF]
, 2006 Luca Capogna, Diego Maldonado
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Existence of infinitely many solutions for critical sub-elliptic systems via genus theory
Communications in Analysis and MechanicsWe are devoted to the study of the following sub-Laplacian system with Hardy-type potentials and critical nonlinearities $ \begin{equation*} \left\{\begin{aligned} -\Delta_{\mathbb{G}}u-\mu_{1}\frac{\psi^{2}u}{\text{d}(z)^{2}} = \lambda_{1}\frac{\psi^{
Hongying Jiao, Shuhai Zhu , Jinguo Zhang
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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
Sub-Riemannian calculus on hypersurfaces in Carnot groups [PDF]
, 2007 Donatella Danielli +2 more
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The Hardy inequality and nonlinear parabolic equations on Carnot groups [PDF]
, 2007 Jerome A. Goldstein, İsmail Kömbe
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A metric boundary theory for Carnot groups [PDF]
arXivIn this paper, we study characteristics of horofunction boundaries of Carnot groups. In particular, we show that for Carnot groups, i.e., stratified nilpotent Lie groups equipped with certain left-invariant homogeneous metrics, all horofunctions are piecewise-defined using Pansu derivatives.
arxiv
Sharp weighted Hardy type inequalities and Hardy–Sobolev type inequalities on polarizable Carnot groups [PDF]
, 2008 Jialin Wang, Pengcheng Niu
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Effects of variable-temperature heat reservoirs on performance of irreversible Carnot refrigerator with heat recovery. [PDF]
Sci Rep, 2023 Zhang Z, Su H, Dai G, Li X, Zeng L.
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