Related papers: Currents in Heisenberg groups
We define currents on a Grassmann algebra $Gr(N)$ with $N$ generators as distributions on its exterior algebra (using the symmetric wedge product). We interpret the currents in terms of ${\Z}_2$-graded Hochschild cohomology and closed…
A current of magnetic moments will flow in the spin-1/2 Heisenberg chain in the presence of an external magnetic field $B$ and a temperature gradient $\Delta T$ along the chain. We show that this magnetothermal effect is strictly {\em…
In this paper we study integer multiplicity rectifiable currents carried by the subgradient (subdifferential) graphs of semi-convex functions on a $n$-dimensional convex domain, and show a weak continuity theorem with respect to pointwise…
The purpose of this study is to analyse two related topics: the Rumin cohomology and the $\mathbb{H}$-orientability in the Heisenberg group $\mathbb{H}^n$. In the first three chapters we carefully describe the Rumin cohomology with…
We consider anisotropic fluids with directional pressures $p_i = w_i \rho$ ($\rho$ is the density, $w_i = $const, $i = 1,2,3$) as sources of gravity in stationary cylindrically symmetric space-times. We describe a general way of obtaining…
By Gromov's compactness theorem for metric spaces, every uniformly compact sequence of metric spaces admits an isometric embedding into a common compact metric space in which a subsequence converges with respect to the Hausdorff distance.…
We present a brief overview of the Kor\'anyi-Reimann theory of quasiconformal mappings on the Heisenberg group stressing on the analogies as well as on the differences between the Heisenberg group case and the classical two-dimensional…
We develop a group-theoretical approach to the formulation of generalized abelian gauge theories, such as those appearing in string theory and M-theory. We explore several applications of this approach. First, we show that there is an…
This paper first proposes a new approximate scheme to construct a harmonic heat flow $u$ between a parabolic cylinder to a sphere. Y.Chen and M.Struwe have proved an existence and discussed a partial regularity of harmonic heat flows by…
We observe that upper densities and spherical Federer densities may differ on all two dimensional surfaces of the sub-Riemannian Heisenberg group. This provides an entire class of intrinsic rectifiable sets having upper density strictly…
A previously found definition of complexity for spherically symmetric fluid distributions [1], is extended to axially symmetric static sources. In this case there are three different complexity factors, defined in terms of three structure…
Many conformal quiver gauge theories admit nonconformal generalizations. These generalizations change the rank of some of the gauge groups in a consistent way, inducing a running in the gauge couplings. We find a group of discrete…
We consider the inverse mean curvature flow (IMCF) in the Heisenberg group $(\He^n, d_\varepsilon)$, where $d_\varepsilon$ is distance associated to either $| \cdot |_\varepsilon$, $\varepsilon>0$, the natural family of left-invariant…
We define and study the harmonic curves on domains in $\mathbb{R}^n$ into the first Heisenberg group $\mathbb{H}^1$. These are the $C^2$-regular mappings which are critical points of the second Dirichlet energy and satisfy the weak…
The effects of the Ohmic and magnetic density currents are investigated in the linearized Euler-Heisenberg electrodynamics. The linearization is introduced through an external magnetic field, in which the vector potential of the…
We classify the entire minimal vertical graphs in the 3 dimensional Heisenberg group Nil endowed with a Riemannian left-invariant metric. This classification, which provides a solution to the Bernstein problem in Nil, is given in terms of…
I present a currents algebra for the two-sites Bose-Hubbard model, generalize the Heisenberg equation of motion to write the second time derivative of the currents operators and use it to get the quantum dynamics of the currents. For…
Triad resonances for gravity waves propagating in opposite direction with respect to uniform current are introduced. They are produced by multivalued and anisotropic dispersion and occur even in deep water. In contrast, existing literature…
Geometrical flows (GF) play an important role in modern mathematics and physics. In this letter we have considered some integrable isotropic GF -- Ricci flows (RF) and mean curvature flows (MCF) -- which are related with integrable…
As we all know, the Minkowski type problem is the cornerstone of the Brunn-Minkowski theory in Euclidean space. The Heisenberg group as a sub-Riemannian space is the simplest non-Abelian degenerate Riemannian space that is completely…