14 citations · 37 across the 33 of their papers we have counts for
6 papers · 2 filters
Subharmonic Functions, Conformal Metrics, and CAT(0)
David A. Herron, Gaven J. Martin
We present an analytical proof that certain natural metric planar universal covers are Hadamard metric spaces. In particular if where is locally Lipschitz and subh…
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…
Quasihyperbolic Metric Universal Covers
David A. Herron, Gaven J. Martin
We present a simple analytical proof that the natural metric universal cover of a quasihyperbolic planar domain is a complete Hadamard metric space.
New models for deformations: Linear Distortion and the failure of rank-one convexity
Seyed Mohsen Hashemi, Gaven J. Martin
In this article, we discuss new models for static nonlinear deformations via scale-invariant conformal energy functionals based on the linear distortion. In particular, we give exa…
Nondiscrete parabolic characters of the free group : supergroup density and Nielsen classes in the complement of the Riley slice
Gaven Martin
A parabolic representation of the free group is one in which the images of both generators are parabolic elements of $PSL(2,\IC)$. The Riley slice is a closed subset ${\cal R…