Results 91 to 100 of about 2,300 (225)
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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A universal heat semigroup characterisation of Sobolev and BV spaces in Carnot groups [PDF]
, 2022 Nicola Garofalo, Giulio Tralli
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Curvature‐dimension condition of sub‐Riemannian α$\alpha$‐Grushin half‐spaces
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract We provide new examples of sub‐Riemannian manifolds with boundary equipped with a smooth measure that satisfy the RCD(K,N)$\mathsf {RCD}(K, N)$ condition. They are constructed by equipping the half‐plane, the hemisphere and the hyperbolic half‐plane with a two‐dimensional almost‐Riemannian structure and a measure that vanishes on their ...
Samuël Borza, Kenshiro Tashiro
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Local Monotonicity and Isoperimetric Inequality on Hypersurfaces in Carnot groups
Bruno Pini Mathematical Analysis Seminar, 2010 Let G be a k-step Carnot group of homogeneous dimension Q. Later on we shall present some of the results recently obtained in [32] and, in particular, an intrinsic isoperimetric inequality for a C2-smooth compact hypersurface S with boundary @S.
Francesco Paolo Montefalcone
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Lusin approximation for horizontal curves in step 2 Carnot groups [PDF]
, 2016 Enrico Le Donne, Gareth Speight
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A note on lifting of Carnot groups
Revista Matemática Iberoamericana, 2005 We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.
BONFIGLIOLI, ANDREA, UGUZZONI, FRANCESCO
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Nonlinear elliptic equations on Carnot groups [PDF]
, 2016 Massimiliano Ferrara +5 more
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Conformal maps of Carnot groups
Annales Academiae Scientiarum Fennicae Mathematica, 2015 If f is a conformal mapping defined on a connected open subset of a Carnot group G, then either f is the composition of a translation, a dilation and an isometry, or G is the nilpotent Iwasawa component of a real rank 1 simple Lie group S, and f arises from the action of S on G, viewed as an open subset of S/P, where P is a parabolic subgroup of G and ...
Cowling, MG, Ottazzi, A
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Exceptional sets for self-similar fractals in Carnot groups [PDF]
, 2010 Zoltán M. Balogh +3 more
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