Euclidean and hyperbolic lenghs of images of arcs

Details Euclidean and hyperbolic lenghs of images of arcs Euclidean and hyperbolic lenghs of images of arcs

2007-11-01

arxiv.org/abs/0711.0219v1

Mathematics

Complex Variables

26 pages

Scientific paper

Let $f$ be a function that is analytic in the unit disc. We give new
estimates, and new proofs of existing estimates, of the Euclidean length of the
image under $f$ of a radial segment in the unit disc. Our methods are based on
the hyperbolic geometry of plane domains, and we address some new questions
that follow naturally from this approach.

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