Constant angle surfaces in the Lorentzian Heisenberg group
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DOI: 10.1007/s00013-017-1104-6
Abstract: In this paper, we define and, then, we characterize constant angle spacelike and timelike surfaces in the three-dimensional Heisenberg group, equipped with a 1-parameter family of Lorentzian metrics. In particular, we give an explicit local… read more here.
Keywords: angle surfaces; heisenberg group; constant angle;
An Explicit Formula for Szegő Kernels on the Heisenberg Group
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DOI: 10.1007/s10114-018-7324-2
Abstract: In this paper, we give an explicit formula for the Szegő kernel for (0, q) forms on the Heisenberg group Hn+1. read more here.
Keywords: explicit formula; szeg kernels; formula szeg; heisenberg group ... See more keywords
The k-plane transform on the Heisenberg group
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DOI: 10.1007/s11868-019-00314-1
Abstract: The paper deals with the k-plane transform $${\mathcal {R}}_{k}$$ on the Heisenberg group. We study the properties of the transform $${\mathcal {R}}_{k}$$ and obtain three types of inversion formulas for $${\mathcal {R}}_{k}$$. The first inversion… read more here.
Keywords: transform heisenberg; group; heisenberg group; heisenberg ... See more keywords
The isoperimetric problem in the Heisenberg group $$\pmb {\mathbb {H}^n}$$ with density
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DOI: 10.1007/s13324-020-00367-2
Abstract: We study the isoperimetric problem for the axially symmetric sets in the Heisenberg group $$\mathbb {H}^n$$ with density $$|z|^p$$ . At first, we prove the existence of weighted isoperimetric sets. Then, we characterize weighted isoperimetric… read more here.
Keywords: mathbb density; isoperimetric problem; heisenberg group; density ... See more keywords
An integral type Brezis-Nirenberg problem on the Heisenberg group
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DOI: 10.1016/j.jde.2020.03.032
Abstract: Abstract This paper is devoted to a class of integral type Brezis-Nirenbreg problems on the Heisenberg group. They are a class of nonlinear integral equations on the bounded domains of Heisenberg group and related to… read more here.
Keywords: type brezis; group; heisenberg group; integral type ... See more keywords
Existence of extremal functions for the Stein–Weiss inequalities on the Heisenberg group
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DOI: 10.1016/j.jfa.2019.01.002
Abstract: In this paper, we establish the existence of extremals for two kinds of Stein-Weiss inequalities on the Heisenberg group. More precisely, we prove the existence of extremals for the Stein-Weiss inequalities with full weights in… read more here.
Keywords: heisenberg group; inequalities heisenberg; existence; stein weiss ... See more keywords
Existence of solutions for Kirchhoff type systems involving Q-Laplacian operator in Heisenberg group
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DOI: 10.1016/j.jmaa.2020.124727
Abstract: Abstract Let H n be the Heisenberg group, Q = 2 n + 2 be the homogeneous dimension of H n , we study the existence of solutions for the following Q-Laplacian elliptic system {… read more here.
Keywords: kirchhoff type; group; heisenberg group; solutions kirchhoff ... See more keywords
Subelliptic equations with singular nonlinearities on the Heisenberg group
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DOI: 10.1186/s13661-018-0925-y
Abstract: AbstractIn this paper, we consider the Dirichlet boundary value problem to singular semilinear subelliptic equation on the Heisenberg group −ΔHu=1uγ+f(u),γ>0.$$-\Delta_{\mathbb{H}}u=\frac{1}{u^{\gamma}}+f(u), \quad \gamma>0. $$ We prove the positivity and continuity up to the boundary for the… read more here.
Keywords: subelliptic equations; equations singular; singular nonlinearities; group ... See more keywords
Applications of Integral Geometry to Geometric Properties of Sets in the 3D-Heisenberg Group
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DOI: 10.1515/agms-2016-0020
Abstract: Abstract By studying the group of rigid motions, PSH(1), in the 3D-Heisenberg group H1,we define a density and a measure in the set of horizontal lines. We show that the volume of a convex domain… read more here.
Keywords: applications integral; group; heisenberg group; geometry ... See more keywords
Intersections of Projections and Slicing Theorems for the Isotropic Grassmannian and the Heisenberg group
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DOI: 10.1515/agms-2020-0002
Abstract: Abstract This paper studies the Hausdorff dimension of the intersection of isotropic projections of subsets of ℝ2n, as well as dimension of intersections of sets with isotropic planes. It is shown that if A and… read more here.
Keywords: intersections projections; slicing theorems; group; heisenberg group ... See more keywords
Minimal translation surfaces in the three-dimensional Heisenberg group
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DOI: 10.2298/fil1906583r
Abstract: We define and classify minimal translation surfaces in the 3-dimensional Heisenberg group H(1,1). read more here.
Keywords: heisenberg group; dimensional heisenberg; minimal translation; translation surfaces ... See more keywords