Upper bounds for value distribution of quasimeromorphic maps
Abstract
Chapters 1 and 2 contain an upper bound on the ratio the counting function and its spherical average. For a quasiregular mapping f: $\IR\sp{n} \to \=\IR\sp{n}$ this gives a converse to (Rickman's generalization of) Nevanlinna's defect relation. Chapter 3 gives an extremal length proof of Burdzy's recent theorem which provides necessary and sufficient conditions for the existence of an angular derivative. The main tool for both problems is the modulus of path families.
Degree
Ph.D.
Advisors
Drasin, Purdue University.
Subject Area
Mathematics
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