Euclidean and hyperbolic lenghs of images of arcs

Abstract

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.

arXiv comment26 pages

Cited by in corpus (3)

• A proof of Hall's conjecture on length of ray images under starlike mappings of order $\alpha$
• Spherical and hyperbolic lengths of images of arcs
• Boundary behaviour of universal covering maps