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math.MG2017★ 1 cited
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…
math.MG2016
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…