Forgetful mappings between Teichmuller spaces.

Title: Forgetful mappings between Teichmuller spaces.
Identifier: AAI9946146
identifier: 9946146
Creator: Bulatovic, Aleksandar.
Contributor: Adviser: Frederick Gardiner
Date: 1999
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: We study holomorphic motions and conformal metrics on hyperbolic Riemann surfaces. We state and prove the extension of holomorphic motions theorem for arbitrary hyperbolic Riemann surface. We then use the results obtained to compare the hyperbolic metric with the metric induced by extremal point shift mappings. We show that the lengths, induced by these metrics, of any rectifiable curve are equal. At the end of this part we prove that two metrics coincide if and only if fibers of "puncture forgetful" maps are in fact Teichmuller disks. We study certain extremal. problems in the Riemann sphere with the unit lattice removed. We give a useful criteria for quasiconformal map, defined on the Riemann sphere with the unit lattice removed, to be extremal.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.