{"id":{"repo_id":"soton","oai_identifier":"oai:eprints.soton.ac.uk:66335"},"canonical_url":"https://search.dev.ndltd.org/etd/soton/oai:eprints.soton.ac.uk:66335","repository":{"repo_id":"soton","name":"University of Southampton","base_url":"https://eprints.soton.ac.uk/cgi/oai2"},"display":{"title":"Classical and non-classical Schottky groups","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Williams, Jonathan Peter"],"institution":"University of Southampton","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Anderson, Jim"],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-02","date_published":"2009-02","updated_at":"2026-07-24T04:36:02Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Anderson, Jim"]},{"key":"dc:creator","label":"Author","values":["Williams, Jonathan Peter"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2009-02"]},{"key":"dc:date.issued","label":"Date","values":["2009-02"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Pure Mathematics (pre 2011 reorg)","School of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Southampton"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://eprints.soton.ac.uk/66335/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Ph.D."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://eprints.soton.ac.uk/66335/1/Jon_Williams_PhD_Thesis.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format","label":"Dc Format","values":["text"]},{"key":"dc:title","label":"Title","values":["Classical and non-classical Schottky groups"]}]}],"canonical_facts":{"dc:contributor.advisor":["Anderson, Jim"],"dc:creator":["Williams, Jonathan Peter"],"dc:date":["2009-02"],"dc:date.issued":["2009-02"],"dc:description.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."],"dc:format":["text"],"dc:identifier.uri":["https://eprints.soton.ac.uk/66335/1/Jon_Williams_PhD_Thesis.pdf"],"dc:publisher.department":["Pure Mathematics (pre 2011 reorg)","School of Mathematics"],"dc:publisher.institution":["University of Southampton"],"dc:relation.isreferencedby":["https://eprints.soton.ac.uk/66335/"],"dc:title":["Classical and non-classical Schottky groups"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["Ph.D."]},"updated_at":"2026-07-24T04:36:02Z"}