8 citations · 18 across the 15 of their papers we have counts for
4 papers · 1 filter
Intrinsic circle domains
Edward Crane
Using quasiconformal mappings, we prove that any Riemann surface of finite connectivity and finite genus is conformally equivalent to an intrinsic circle domain U in a compact Riem…
A note on the Hayman-Wu theorem
Edward Crane
The Hayman-Wu theorem states that the preimage of a line or circle L under a conformal mapping from the unit disc to a simply-connected domain U has total Euclidean length bounded…
Mean Value Conjectures for Rational Maps
Edward Crane
Let p be a polynomial in one complex variable. Smale's mean value conjecture estimates |p'(z)| in terms of the gradient of a chord from (z, p(z)) to some stationary point on the gr…
The Area of Polynomial Images and Preimages
Edward Crane
Let p be a monic polynomial in one complex variable and K a measurable subset of the complex plane. In terms of the area of K, we give an upper bound on the area of the preimage of…