Results 1 to 10 of about 12,584,112 (314)

On the Dimension of Kakeya Sets in the First Heisenberg Group [PDF]

arXiv, 2021
We define Kakeya sets in the Heisenberg group and show that the Heisenberg Hausdorff dimension of Kakeya sets in the first Heisenberg group is at least 3. This lower bound is sharp since, under our definition, the $\{xoy\}$-plane is a Kakeya set with Heisenberg Hausdorff dimension 3.
Jiayin Liu
arxiv   +3 more sources

Critical nonlocal Schrödinger-Poisson system on the Heisenberg group

Advances in Nonlinear Analysis, 2021
In this paper, we are concerned with the following a new critical nonlocal Schrödinger-Poisson system on the Heisenberg group:
Liu Zeyi, Tao Lulu, Zhang Deli, Liang Sihua, Song Yueqiang   +4 more
doaj   +2 more sources

Concentration-compactness results for systems in the Heisenberg group [PDF]

Opuscula Mathematica, 2020
In this paper we complete the study started in [P. Pucci, L. Temperini, Existence for (p,q) critical systems in the Heisenberg group, Adv. Nonlinear Anal.
Patrizia Pucci, Letizia Temperini
doaj   +2 more sources

Existence for (p, q) critical systems in the Heisenberg group

Advances in Nonlinear Analysis, 2019
This paper deals with the existence of entire nontrivial solutions for critical quasilinear systems (𝓢) in the Heisenberg group ℍn, driven by general (p, q) elliptic operators of Marcellini types.
Pucci Patrizia, Temperini Letizia
doaj   +2 more sources

Height zeta functions of equivariant compactifications of the Heisenberg group [PDF]

arXiv, 2002
We study analytic properties of height zeta functions of equivariant compactifications of the Heisenberg group.
J. A. Shalika, Yuri Tschinkel
arxiv   +3 more sources

Intrusion of quantum crystallography into classical lands. [PDF]

Acta Crystallogr B Struct Sci Cryst Eng Mater
One hundred years after the quantum theory established position and momentum as incompatible quantities, quantum crystallography offers a way to visualize electron phase space behaviour in crystals.This article, written on the occasion of the International Year of Quantum Science and Technology, explores the development of alternative approaches to ...
Yu S, Gillet JM.
europepmc   +2 more sources

Nonlocal Harnack inequalities in the Heisenberg group [PDF]

Calculus of Variations and Partial Differential Equations, 2022
We deal with a wide class of nonlinear integro-differential problems in the Heisenberg-Weyl group Hn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage ...
Giampiero Palatucci, Mirco Piccinini
semanticscholar   +1 more source

Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group [PDF]

Journal of Geometric Analysis, 2022
We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p -Laplacian operator on the Heisenberg-Weyl group $$\mathbb
M. Manfredini, Giampiero Palatucci, Mirco Piccinini, S. Polidoro   +3 more
semanticscholar   +1 more source

On the critical Choquard-Kirchhoff problem on the Heisenberg group

Advances in Nonlinear Analysis, 2022
In this paper, we deal with the following critical Choquard-Kirchhoff problem on the Heisenberg group of the form: M ( ‖ u ‖ 2 ) ( − Δ H u + V ( ξ ) u ) = ∫ H N ∣ u ( η ) ∣ Q λ ∗ ∣ η − 1 ξ ∣ λ d η ∣ u ∣ Q λ ∗ − 2 u + μ f ( ξ , u ) , M\left(\Vert u{\Vert }
Xueqi Sun, Yueqiang Song, Sihua Liang
semanticscholar   +1 more source

Campana points on biequivariant compactifications of the Heisenberg group [PDF]

European Journal of Mathematics, 2020
We study Campana points on biequivariant compactifications of the Heisenberg group and confirm the log Manin conjecture introduced by Pieropan, Smeets, Tanimoto and Várilly-Alvarado.
Huan Xiao
semanticscholar   +1 more source