14 citations · 37 across the 33 of their papers we have counts for
40 papers
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…
Topological regularity for solutions to the generalised Hopf equation
Gaven Martin, Cong Yao
The generalised Hopf equation is the first order nonlinear equation with data a holomorphic functions and a positive weight, \[ h_w\,\overline{h_\wbar}\,η(w) = Φ.\] T…
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…
On the uniqueness of extremal mappings of finite distortion
Gaven Martin, Cong Yao
For an arbitrary convex function , we consider uniqueness in the following two related extremal problems: Problem A boundary value problem: Establish t…
Concrete one complex dimensional moduli spaces of hyperbolic manifolds and orbifolds
Alex Elzenaar, Gaven Martin, Jeroen Schillewaert
The Riley slice is arguably the simplest example of a moduli space of Kleinian groups; it is naturally embedded in , and has a natural coordinate system (introduced b…