Classical and non-classical Schottky groups

This thesis looks at two disparate problems relating to Schottky groups, and in particular what it means for a Schottky group to be classical or non- classical. The first problem focusses ofl the uniformization of R.iemann surfaces using Schottky groups. We extend the retrosection theorem of Koebe by giving conditions on lengths of curves as to when a Riemann surface can be uniformized by a classical Schottky group. The second section of this thesis examines a paper of Yamamoto ([40]), which gives the first example of a non-classical Schottky group. We firstly expand on the detail given in the paper, and then use this to give a second example of a non-classical Schottky group. We then take tIns second example and generalise to a two-variable family of non-classical Schottky groups.

Name dc:type.qualificationname

Ph.D.

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

University of Southampton

Year dc:date.issued

2009

Author dc:creator

• Williams, Jonathan Peter

Advisor dc:contributor.advisor

• Anderson, Jim