相关论文: Geodetically convex sets in the Heisenberg group $…

Let $\mathbb{H}$ be the three-dimensional Heisenberg group. We introduce a structure on the Heisenberg group which consists of the biregular representation of $\mathbb{H\times H}$ restricted to some discrete subset of $\mathbb{H\times H}$…

We classify the isoparametric functions on $\mathbb{R}^n\times\mathbb{M}^m$, $n, m\geq2$, with compact level sets, where $\mathbb{M}^m$ is a connected, closed Riemannian manifold of dimension $m$. Also, we classify the isoparametric…

A class of well-behaved *-representations of a q-deformed Heisenberg algebra is studied and classified.

We define the Grothendieck group of an n-angulated category and show that for odd n its properties are as in the special case of n=3, i.e. the triangulated case. In particular, its subgroups classify the dense and complete n-angulated…

Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this…

These notes treat a momentum map associated to the Heisenberg group. We classify the coadjoint orbits of the Heisenberg group and show that the cocycle associated to the momentum map becomes a value of the modulus of a coadjoint orbit. We…

We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a…

We prove that any $C^2$ complete, orientable, connected, stable area-stationary surface in the sub-Riemannian Heisenberg group $\mathbb{H}^1$ is either a Euclidean plane or congruent to the hyperbolic paraboloid $t=xy$.

In these notes we construct a quantization functor, associating an Hilbert space H(V) to a finite dimensional symplectic vector space V over a finite field F_q. As a result, we obtain a canonical model for the Weil representation of the…

Given a real-valued function $c$ defined on the cartesian product of a generic Carnot group $\G$ and the first layer $V_1$ of its Lie algebra, we introduce a notion of $c$ horizontal convex ($c$ H-convex) function on $\G$ as the supremum of…

We prove a rank-one theorem \`a la G. Alberti for the derivatives of vector-valued maps with bounded variation in a class of Carnot groups that includes Heisenberg groups $\mathbb H^n$ for $n\geq 2$. The main tools are properties relating…

We give an overview of how to construct continued fractions on the Heisenberg group $\mathbb{H}$, the projective and planar Siegel models of the group, and how to perform computations on the group using matrices. We discuss and work with…

In this paper, we obtained some inequalities for \phi_{s}-convex function, \phi-Godunova-Levin function, \phi-P-function and log-\phi-convex function. Finally, we defined the class of \phi-quasi-convex functions and we examined some…

We derive explicit formulae for the subalgebra zeta functions of all higher Heisenberg Lie algebras over an arbitrary compact discrete valuation ring $\mathfrak{o}$. To this end, we develop Hecke-theoretic techniques for the enumeration, by…

We characterize $p-$harmonic functions in the Heisenberg group in terms of an asymptotic mean value property, where $1<p<\infty$, following the scheme described in Manfredi et al. (2009) for the Euclidean case. The new tool that allows us…

We explore the connection between the notion of Hopf category and the categorification of the infinite dimensional Heisenberg algebra via graphical calculus proposed by M.Khovanov. We show that the existence of a Hopf structure on a…

We consider (bounded) Besicovitch sets in the Heisenberg group and prove that $L^p$ estimates for the Kakeya maximal function imply lower bounds for their Heisenberg Hausdorff dimension.

We consider $H$(eisenberg)-type groups whose law of left translation gives rise to a bracket generating distribution of step 2. In the contrast with sub-Riemannian studies we furnish the horizontal distribution with a nondegenerate…

In the sub-Riemannian Heisenberg group equipped with its Carnot-Caratheodory metric and with a Haar measure, we consider isodiametric sets, i.e. sets maximizing the measure among all sets with a given diameter. In particular, given an…

For a closed symplectic manifold $(M,\omega)$ with compatible Riemannian metric $g$ we study the Sobolev $H^1$ geometry of the group of all $H^s$ diffeomorphisms on $M$ which preserve the symplectic structure. We show that, for sufficiently…