Classical and non-classical Schottky groups
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.
Williams, Jonathan Peter
350a1e81-f31b-404f-861b-d48c18eb2fd6
February 2009
Williams, Jonathan Peter
350a1e81-f31b-404f-861b-d48c18eb2fd6
Anderson, Jim
739c0e33-ef61-4502-a675-575d08ee1a98
Williams, Jonathan Peter
(2009)
Classical and non-classical Schottky groups.
University of Southampton, School of Mathematics, Doctoral Thesis, 125pp.
Record type:
Thesis
(Doctoral)
Abstract
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.
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Published date: February 2009
Organisations:
University of Southampton
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Local EPrints ID: 66335
URI: http://eprints.soton.ac.uk/id/eprint/66335
PURE UUID: b84e2df7-5cb2-4ebc-9656-df8281bb78ae
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Date deposited: 04 Jun 2009
Last modified: 14 Mar 2024 02:39
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Author:
Jonathan Peter Williams
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