14 citations · 37 across the 33 of their papers we have counts for
26 papers · 1 filter
Examples of Uniformly Quasiregular Mappings with Fatou Set Having Infinitely Many Components
Gaven Martin, Kirsi Peltonen
We construct examples of uniformly quasiregular mappings (uqr) acting on a sphere and having Fatou set consisting of infinitely many components. In particular we construct a uqr ma…
On the Conformal Energy of Quasisymmetric and Quasimöbius Mappings
Mihai Florincescu, Gaven Martin
This article identifies the conformal energy (or mean distortion) of extremal mappings of finite distortion with a given quasisymmetric mapping of the circle as boundary data. The…
The Generic Failure of Lower-semicontinuity for the Linear Distortion Functional
Sayed Mohsen Hashemi, Gaven J. Martin
We consider the convexity properties of distortion functionals, particularly the linear distortion, defined for homeomorphisms of domains in Euclidean -spaces, . The in…
Energy-minimal Principles in Geometric Function Theory
Tadeusz Iwaniec, Gaven Martin, Jani Onninen
We survey a number of recent developments in geometric analysis as they pertain to the calculus of variations and extremal problems in geometric function theory following the NZMRI…
The Teichmüller problem for -means of distortion
Gaven J. Martin, Cong Yao
Teichmüller's problem from 1944 is this: Given find and describe the extremal quasiconformal map $f:\ID\to\ID$, $f|\partial \ID=identity$ and . We consi…
Projections in moduli spaces of Kleinian groups
Hala Alaqad, Jianhua Gong, Gaven Martin
A two-generator Kleinian group can be naturally associated with a discrete group with the generator of order and where \begin{equ…