Samuel Dillon

Citation

Thesis Title
Resolving Decomposition By Blowing Up Points And Quasiconformal Harmonic Extensions

Read article at Massey Research Online:

We investigate mappings of finite distortion which both blow up a point in a two-dimensional space equipped with a radially symmetric metric and which lie in some Lebesgue p-space, proving a lower bound on the appropriate norm. We apply this result to the resolution of decomposition which arise in the study of Kleinian groups and iterations of rational maps; proving another result which limits the p where we can find mappings of a certain form which shrink the unit interval to a point and whose inverse has distortion in the Lebesgue p-space. We also construct a nonlinear inhomogeneous Beltrami equation equivalent to the Schoen conjecture of quasiconformal harmonic extensions.

Supervisors
Distinguished Professor Gaven Martin
Professor Carlo Laing