Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Warhurst, Ben"'
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 isotropicity condi
Externí odkaz:
http://arxiv.org/abs/2407.20029
We solve the contact equivalence problem for generalised sub-Laplacians on $\He^2$ and show that the family of sub-Laplacians on $\He^2$ modulo contact equivalence, is parameterised by $\R^+$
Externí odkaz:
http://arxiv.org/abs/2310.05586
Autor:
Adamowicz, Tomasz, Warhurst, Ben
We study various notions of the Schwarzian derivative for contact mappings in the Heisenberg group $\mathbb{H}_1$ and introduce two definitions: (1) the CR Schwarzian derivative based on the conformal connection approach studied by Osgood and Stowe a
Externí odkaz:
http://arxiv.org/abs/2110.06670
Autor:
Warhurst, Ben
Motivated by recent interest concerning "puncture repair" in the conformal geometry of compact Riemannian manifolds, a brief exposition on generalisation to the setting of quasiconformal mappings on certain metric measure spaces is presented as well
Externí odkaz:
http://arxiv.org/abs/1801.05484
We prove a Koebe distortion theorem for the average derivative of a quasiconformal mapping between domains in the sub-Riemannian Heisenberg group $\mathbb{H}_1$. Several auxiliary properties of quasiconformal mappings between subdomains of $\mathbb{H
Externí odkaz:
http://arxiv.org/abs/1707.02832
Autor:
Adamowicz, Tomasz, Warhurst, Ben
We study strongly harmonic functions in Carnot-Carath\'eodory groups defined via the mean value property with respect to the Lebesgue measure. For such functions we show their Sobolev regularity and smoothness. Moreover, we prove that strongly harmon
Externí odkaz:
http://arxiv.org/abs/1702.07642
We provide a classification of $ts$-invariant sub-Lorentzian structures on $3$ dimensional contact Lie groups. Our approach is based on invariants arising form the construction of a normal Cartan connection.
Externí odkaz:
http://arxiv.org/abs/1602.05091
Autor:
Adamowicz, Tomasz, Warhurst, Ben
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 is defined via uniform domains and the Loewner property. Using prime ends
Externí odkaz:
http://arxiv.org/abs/1512.09165
Autor:
Grochowski, Marek, Warhurst, Ben
Publikováno v:
SIGMA 11 (2015), 031, 23 pages
In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector fields whi
Externí odkaz:
http://arxiv.org/abs/1312.4581