29 citations · 40 across the 8 of their papers we have counts for
9 papers
Existence of quasiconformal maps with maximal stretching on any given countable set
Rosemarie Bongers, James T. Gill
Quasiconformal maps are homeomorphisms with useful local distortion inequalities; infinitesimally, they map balls to ellipsoids with bounded eccentricity. This leads to a number of…
Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spaces
Sylvester Eriksson-Bique, James T. Gill, Panu Lahti +1
In this paper, we study the asymptotic behavior of BV functions in complete metric measure spaces equipped with a doubling measure supporting a -Poincaré inequality. We show tha…
Discrete Approximations of Metric Measure Spaces of Controlled Geometry
James T. Gill, Marcos Lopez
We find a necessary and sufficient condition for a doubling metric space to carry a (1,p)-Poincare inequality. The condition involves discretizations of the metric space and Poinca…
Geometric analysis on Cantor sets and trees
Anders Björn, Jana Björn, James T. Gill +1
Using uniformization, Cantor type sets can be regarded as boundaries of rooted trees. In this setting, we show that the trace of a first-order Sobolev space on the boundary of a re…
A note on quasiconformal maps with Holder-continuous dilatation
James T. Gill, Steffen Rohde
Here we give an alternate proof of a sufficient condition due to J. Mateu, J. Orobitg, and J. Verdera for a quasiconformal map of the plane with dilatation supported in a smooth do…
Doubling Metric Spaces are Characterized by a Lemma of Benjamini and Schramm
James T. Gill
A useful property of Euclidean space originally shown by I. Benjamini and O. Schramm turns out to characterize doubling metric spaces.