Alastair N. Fletcher

Sobolev mixing constants and compactness in rational moduli space

We study uniformity of Sobolev mixing estimates for rational maps and uniformly quasiregular mappings. For rational maps of fixed degree, the optimal centered Sobolev trace constant $A_f$ is a continuous proper function on M\"obius moduli space. Uniform bounds on $A_f$ therefore characterize relative compactness in mod...