Escaping nontangentiality: Towards a controlled tangential amortized Julia-Carathéodory theory

J. E. Pascoe, Meredith Sargent, Ryan Tully-Doyle

Let $f:D\to \Omega$ be a complex analytic function. The Julia quotient is given by the ratio between the distance of $f(z)$ to the boundary of $\Omega$ and the distance of $z$ to t…