1 citations · 1 across the 1 of their papers we have counts for
6 papers
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…
Hyperbolic Distance versus Quasihyperbolic Distance in Plane Domains
David A Herron, Jeff Lindquist
We examine Euclidean plane domains with their hyperbolic or quasihyperbolic distance. We prove that the associated metric spaces are quasisymmetrically equivalent if and only if th…
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.
Quasihyperbolic geodesics are hyperbolic quasi-geodesics
David A Herron, Stephen M Buckley
This is a tale describing the large scale geometry of Euclidean plane domains with their hyperbolic or quasihyperbolic distances. We prove that in any hyperbolic plane domain, hype…
Quasiconvexity in the Heisenberg group
David A. Herron, Anton Lukyanenko, Jeremy T. Tyson
We show that if is a closed subset of the Heisenberg group whose vertical projections are nowhere dense, then the complement of is quasiconvex. In particular, closed sets w…
Quasicircles and Bounded Turning Circles Modulo bi-Lipschitz Maps
David A. Herron, Daniel Meyer
We construct a catalog, of snowflake type metric circles, that describes all metric quasicircles up to \bl\ equivalence. This is a metric space analog of a result due to Rohde. Our…