2 citations · 2 across the 4 of their papers we have counts for
4 papers
Conical limit sets and continued fractions
Edward Crane, Ian Short
Inspired by questions of convergence in continued fraction theory, Erdős, Piranian and Thron studied the possible sets of divergence for arbitrary sequences of Möbius maps acting o…
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…