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...
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University of Southampton
2009
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| Online Access: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.500844 |
| Summary: | 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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