Results 61 to 68 of about 371 (68)

Intrinsic Lipschitz graphs in Carnot groups of step 2 [PDF]

arXiv, 2019
We focus our attention on the notion of intrinsic Lipschitz graphs, inside a special class of metric spaces i.e. the Carnot groups. More precisely, we provide a characterization of locally intrinsic Lipschitz functions in Carnot groups of step 2 in terms of their intrinsic distributional gradients.
arxiv  

Sharp Hardy-Littlewood-Sobolev Inequalities on Octonionic Heisenberg Group [PDF]

arXiv, 2014
This paper is a second one following our work [CLZ13] in series, considering sharp Hardy- Littlewood-Sobolev inequalities on groups of Heisenberg type. The first important breakthrough was made by Frank and Lieb in [FL12]. In this paper, analogous results are obtained for octonionic Heisenberg group.
arxiv  

A Note on Commutators of the Fractional Sub-Laplacian on Carnot Groups [PDF]

arXiv, 2017
In this manuscript, we provide a point-wise estimate for the $3$-commutators involving fractional powers of the sub-Laplacian on Carnot groups of homogeneous dimension $Q$. This can be seen as a fractional Leibniz rule in the sub-elliptic setting.
arxiv  

Curvature estimates for minimal hypersurfaces in the Heisenberg group [PDF]

arXiv
In this paper we solve the Bernstein problem for a broad class of smooth, non-characteristic hypersurfaces in the second sub-Riemannian Heisenberg group $\mathbb{H}^2$.
arxiv  

Positive solutions of a critical equation in sub-Finsler geometry

We compute a two-parameter family of explicit positive solutions of a critical Yamabe type equation for a nonlinear operator that sits at the intersection of Finsler and sub-Riemannian geometryComment: arXiv admin note: text overlap with arXiv:2401 ...
Garofalo, Nicola, Salani, Paolo
core  

Uncertainty principles for the imaginary Ornstein-Uhlenbeck operator

We prove two forms of uncertainty principle for the Schr\"odinger group generated by the Ornstein-Uhlenbeck operator. As a consequence, we derive a related (in fact, equivalent) result for the imaginary harmonic oscillator.Comment: Several typos have ...
Garofalo, Nicola
core  

a review of L1-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups by Baldi, Annalisa; Franchi, Bruno; Pansu, Pierre [PDF]

Hirokazu NISHIMURA, 西村 泰一
core   +1 more source