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[{"key": "dc.contributor.advisor", "value": "Rajala, Kai", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Ikonen, Toni", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2017-11-11T17:52:17Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2017-11-11T17:52:17Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2017", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1738390", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/55839", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Riemannin pinnat ja Teichm\u00fcller-teoriaa.\r\n\r\nT\u00e4m\u00e4n ty\u00f6n p\u00e4\u00e4m\u00e4\u00e4r\u00e4n\u00e4 on m\u00e4\u00e4ritell\u00e4 Riemannin pintojen Teichm\u00fcller-avaruudet sek\u00e4 tutkia niiden geometrisia ominaisuuksia. Ensin ty\u00f6ss\u00e4 kehitet\u00e4\u00e4n peiteavaruuksien ja toimintojen teoriaa, jota sovelletaan M\u00f6bius-kuvauksista koostuviin ryhmiin. T\u00e4m\u00e4n j\u00e4lkeen kvasikonformaalikuvaukset m\u00e4\u00e4ritell\u00e4\u00e4n Riemannin pinnoille ja niiden yhteytt\u00e4 yhdesti yhten\u00e4isten Riemannin avaruuksien kvasikonformikuvauksiin tutkitaan. N\u00e4it\u00e4 tietoja sek\u00e4 yhdesti yhten\u00e4isten Riemannin pintojen uniformisaatiolausetta hy\u00f6dynt\u00e4m\u00e4ll\u00e4 todistetaan yleisten Riemannin pintojen uniformisaatiolause. T\u00e4m\u00e4 tulos liitt\u00e4\u00e4 pinnat M\u00f6bius-kuvauksien toimintoihin yhdesti yhten\u00e4isill\u00e4 Riemannin pinnoilla.\r\n\r\nYleisten Riemannin pintojen uniformaatioteoreema mahdollistaa ty\u00f6ss\u00e4 k\u00e4ytetyt Teichm\u00fcllerin avaruuksien m\u00e4\u00e4ritelm\u00e4t. N\u00e4ille avaruuksille annetaan useampi\r\nekvivalentti m\u00e4\u00e4ritelm\u00e4. T\u00e4m\u00e4n j\u00e4lkeen Teichm\u00fcllerin avaruuksiin m\u00e4\u00e4ritell\u00e4\u00e4n\r\nteorian kannalta luonnollinen et\u00e4isyysfunktio, joka tekee avaruuksista geodeettisen ja t\u00e4ydellisen. Lis\u00e4ksi osoitetaan ett\u00e4 Riemannin pintojen v\u00e4liset kvasikonformaalikuvaukset indusoivat surjektiivisen isometrian pintojen Teichm\u00fcllerin avaruuksien v\u00e4lille. Lopuksi yhdesti yhten\u00e4isten Riemannin pintojen, punkteerattujen kompaktien Riemannin pintojen sek\u00e4 topologisten sylintereiden Teichm\u00fcller-avaruudet karakterisoidaan. Yhdesti yhten\u00e4isist\u00e4 pinnoista vain hyperbolisella tasolla osoittautuu olevan ep\u00e4triviaali Teichm\u00fcllerin avaruus. Topologisten sylintereiden tapauksessa havaitaan kolme erilaista Teichm\u00fcllerin avaruutta, jotka vastaavat punkteerattua tasoa, punkteerattua kiekkoa ja rengasta.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "The main objective of this work is to develop the necessary tools to define the Teichm\u00fcller spaces of Riemann surfaces and study their geometric properties. Firstly, some theory of covering spaces and topological actions will be studied and the results applied to M\u00f6bius transformations. Secondly, quasiconformal maps between Riemann surfaces will be defined and they will be characterized using quasiconformal maps between simply-connected Riemann surfaces. These results and the Uniformization Theorem of simply-connected Riemann surfaces will be used to prove a Uniformization Theorem for general Riemann surfaces. Such surfaces will be linked to actions of M\u00f6bius transformations on simply-connected Riemann surfaces.\r\n\r\nThe Uniformization Theorem of Riemann surfaces will be used to define Teichm\u00fcller spaces. A couple of equivalent definitions will be introduced. After that a natural distance function is defined on Teichm\u00fcller spaces which makes them geodesic and complete. It will be shown that quasiconformal maps between Riemann surfaces induce isometries between their Teichm\u00fcller spaces. Finally, the Teichm\u00fcller spaces of Riemann surfaces that are either simply-connected, punctured compact Riemann surfaces, or topological cylinders will be characterized. In the simply-connected case, only the hyperbolic plane has a non-trivial Teichm\u00fcller space. The topological cylinders have three distinct Teichm\u00fcller spaces each of which correspond to exactly one of the following: the once-punctured plane, the once-punctured disk, or annuli.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Toni Ikonen (tomaheik) on 2017-11-11 17:52:17.365867. Form: Pro gradu -lomake (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake). JyX data: [jyx_publishing-allowed (fi) =True]", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija.group@korppi.jyu.fi) on 2017-11-11T17:52:17Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-201711114223.pdf: 654993 bytes, checksum: 37253264496abab3942891348f9ff67b (MD5)\r\nlicense.html: 4793 bytes, checksum: 92e1b6340aaf052acc48e306a82a865b (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2017-11-11T17:52:17Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-201711114223.pdf: 654993 bytes, checksum: 37253264496abab3942891348f9ff67b (MD5)\r\nlicense.html: 4793 bytes, checksum: 92e1b6340aaf052acc48e306a82a865b (MD5)\r\n Previous issue date: 2017", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (78 sivua)", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "peiteavaruus", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "peitekuvaus", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "M\u00f6bius-kuvaukset", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Riemannin pinta", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "kvasikonformikuvaus", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Teichmu\u0308llerin avaruus", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Teichmu\u0308llerin metriikka", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "covering space", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "covering map", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "M\u00f6bius transformation", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Riemann surface", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "quasiconformal map", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Teichmu\u0308ller space", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Teichmu\u0308ller metric", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Riemann surfaces and Teichmu\u0308ller theory", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-201711114223", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.date.updated", "value": "2017-11-11T17:52:18Z", "language": "", "element": "date", "qualifier": "updated", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": 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