Samuel Dillon

Doctor of Philosophy, (Mathematics)
Study Completed: 2013
College of Sciences


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

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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.

Distinguished Professor Gaven Martin
Professor Carlo Laing