We present a new technique for the design of transformation-optics devices based on large-
scale optimization to achieve the optimal effective isotropic dielectric materials within …

We define Hardy spaces H p, 0< p<∞, for quasiconformal mappings on the Korányi unit ball
B in the first Heisenberg group H 1. Our definition is stated in terms of the Heisenberg polar …

We consider the affine-additive group as a metric measure space with a canonical left-
invariant measure and a left-invariant sub-Riemannian metric. We prove that this metric …

We study the families of measures on Carnot groups that have vanishing p-module, which
we call M p-exceptional families. We found necessary and sufficient Conditions for the family …

We investigate prime ends in the Heisenberg group $\mathbb {H} _ {1} $ extending N\" akki's
construction for collared domains in Euclidean spaces. The corresponding class of domains …

The modulus method introduced by H. Grötzsch yields bounds for a mean distortion
functional of quasiconformal maps between two annuli mapping the respective boundary …

In this paper, we are interested in the construction of quasiconformal mappings between
domains of the Heisenberg group $\mathbf {H} $ that minimize a mean distortion functional …

Let H be the sub-Riemannian Heisenberg group. That H supports a rich family of
quasiconformal mappings was demonstrated by Korányi and Reimann using the so-called …

Let $\mathcal {S} $ be a surface of revolution embedded in the Heisenberg group $\mathfrak
{H} $. A revolution ring $ R_ {a, b}(\mathcal {S}) $, $0< a< b $, is a domain in $\mathfrak {H} …

A study of smooth contact quasiconformal mappings of the hyperbolic Heisenberg group is
presented in this paper. Our main result is a Lifting Theorem; according to this, a symplectic …