The Length Spectrum Metric on the Teichmuller Space of a Flute Surface

Title: The Length Spectrum Metric on the Teichmuller Space of a Flute Surface
Identifier: d_2009_2013:3f3bbd27c162:11710
identifier: 12318
Creator: Evren, Ozgur,
Contributor: Ara Basmajian
Date: 2013
Language: English
Publisher: City University of New York.
Subject: Mathematics | Flute Surface | Length Spectrum | Teichmuller
Abstract: The topology defined by the length spectrum metric on the Teichmuller space of an infinite type surface, in contrast to finite type surfaces, need not be the same as the topology defined by the Teichmuller metric. In this thesis, we study the equivalence of these topologies on a particular kind of infinite type surface, called the flute surface. Following a construction by Shiga and using additional hyperbolic geometric estimates, we obtain sufficient conditions in terms of length parameters for these two metrics to be topologically inequivalent. Next, we construct infinite parameter families of quasiconformally distinct flute surfaces, both with fixed and varying boundary data, with the property that the length spectrum metric is not topologically equivalent to the Teichmuller metric.
Type: dissertation
Source: 2009_2013.csv
degree: Ph.D.
Program: Mathematics

Media: The Length Spectrum Metric on the Teichmuller Space of a Flute Surface