HARMONIC MEASURE, EXTREMAL DISTANCE, AND HYPERBOLIC METRICS IN SMOOTH DOMAINS

2008.

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Abstract:

Given a simply connected planar domain Ω we develop estimates for boundary derivatives on∂ Ω and estimates for hyperbolic and extremal distances in Ω and the hyperbolic convex hull boundary SΩ. We are able to obtain very explicit estimates using the geometry of the medial axis. Results include a refinement and proof of the Thurston-Sulliv...More

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