3 citations · 4 across the 10 of their papers we have counts for
11 papers
-Extremal Teichmüller mappings between Riemann surfaces are diffeomorphisms
Gaven Martin, Cong Yao
We consider minimisers in the homotopy class of a homeomorphism between analytically finite Riemann surfaces with minimal - conformal energy \[ \mathsf{E}_p(f:R,S…
Diffeomorphic solutions of Ahlfors-Hopf equations
Gaven Martin, Cong Yao
Here we advance the study of boundary the value problem for extremal functions of mean distortion and the associated Teichmüller spaces interpolating between the classical examples…
On the properness of -conformal energy on the Teichmüller space of a Riemann surface
Hala Alaqad, Jianhua Gong, Gaven Martin +1
We establish that the -conformal energy, , defined by the -norms of the distortion of Sobolev mappings, is a proper functional on the Teichmüller space of Riemann…
The exponential Teichmüller theory: Ahlfors--Hopf differentials and diffeomorphisms
Gaven Martin, Cong Yao
We consider minimisers of the -exponential conformal energy for homeomorphisms of finite distortion $\IK(z,f)$ between analytically finite Riemann surfaces in a fixe…
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…
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…
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…
Extremal mappings of finite distortion and the Radon-Riesz property
Gaven Martin, Cong Yao
We consider Sobolev mappings $f\in W^{1,q}(Ω,\IC)$, , between planar domains $Ω\subset \IC$. We analyse the Radon-Riesz property for convex functionals of the form \[f\…
Higher regularity and uniqueness for inner variational equations
Gaven Martin, Cong Yao
We study local minima of the -conformal energy functionals, \[ \mathsf{E}_{\cal A}^\ast(h):=\int_\ID {\cal A}(\IK(w,h)) \;J(w,h) \; dw,\quad h|_\IS=h_0|_\IS, \] defined for self…
The Teichmüller theory: Existence and regularity of critical points
Gaven Martin, Cong Yao
We study minimisers of the -conformal energy functionals, \[ \mathsf{E}_p(f):=\int_\ID \IK^p(z,f)\,dz,\quad f|_\IS=f_0|_\IS, \] defined for self mappings $f:\ID\to\ID$ with fini…
Non-variational extrema of exponential Teichmüller spaces
Gaven Martin, Cong Yao
The exponential Teichmüller spaces , , interpolate between the classical Teichmüller space () and the space of harmonic diffeomorphisms .…