3 papers
math.CV2020
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…
math.DG2020
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…
math.CV2020
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.