Unique determination of quadratic differentials by their admissible functions
| dc.contributor.author | Kim, Hye Seon | |
| dc.contributor.examiningcommittee | Zorboska, Nina (Mathematics) Gericke, Michael (Physics) | en_US |
| dc.contributor.supervisor | Schippers, Eric (Mathematics) | en_US |
| dc.date.accessioned | 2011-09-28T13:44:40Z | |
| dc.date.available | 2011-09-28T13:44:40Z | |
| dc.date.issued | 2011-09-28 | |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | en_US |
| dc.description.abstract | Let f be an analytic and one-to-one function on the unit disk such that f(0)=0. Let Q(w)dw^2 be a quadratic differential. Suppose that f maps into the complex plane or the unit disk minus analytic arcs w(t) satisfying Q(w(t))(dw/dt)^2<0. We are interested in the question: if Q is unknown but of a specified form, does f determine the quadratic differential Q uniquely? Our main result is that for functions mapping into the unit disk and quadratic differentials with a pole of order 4 at the origin, the quadratic differential is uniquely determined up to exceptional cases. This question arises in the study of extremal functions for functionals over classes of analytic one-to-one maps. | en_US |
| dc.description.note | October 2011 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/4947 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | quadratic | en_US |
| dc.subject | differentials | en_US |
| dc.subject | extremal | en_US |
| dc.subject | admissible | en_US |
| dc.title | Unique determination of quadratic differentials by their admissible functions | en_US |
| dc.type | master thesis | en_US |