14 citations · 37 across the 33 of their papers we have counts for
4 papers · 1 filter
The Geometry and Arithmetic of Kleinian Groups
Gaven J. Martin
In this article we survey and describe various aspects of the geometry and arithmetic of Kleinian groups - discrete nonelementary groups of isometries of hyperbolic -space. In p…
The Theory of Quasiconformal Mappings in Higher Dimensions, I
Gaven J. Martin
We present a survey of the many and various elements of the modern higher-dimensional theory of quasiconformal mappings and their wide and varied application. It is unified (and li…
Harmonic degree 1 maps are diffeomorphisms: Lewy's theorem for curved metrics
Gaven J. Martin
In 1936 H. Lewy showed that the Jacobian determinant of a harmonic homeomorphism between planar domains does not vanish and thus the map is a diffeomorphism. This built on the earl…
The tension equation with holomorphic coefficients, harmonic mappings and rigidity
Gaven J Martin
The tension equation for a mapping is the nonlinear second order equation \[ Δf +φ(f) f_z f_{\bar z} = 0\] Solutions are "harmonic" mappings. Here we…