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[{"key": "dc.contributor.advisor", "value": "Rajala, Kai", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Lepp\u00e4nen, Antti", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2018-08-08T06:41:15Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2018-08-08T06:41:15Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2018", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/59147", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Mostow\u2019n rigiditeettilauseen mukaan kaksi v\u00e4hint\u00e4\u00e4n 3-ulotteista kompaktia hyperbolista monistoa ovat isometriset, jos ne ovat di\ufb00eomor\ufb01set. Hyperbolinen monisto on monisto, jolla on hyperbolisen avaruuden avointen joukkojen kanssa isometrisist\u00e4 avoimista joukoista koostuva peite. George Mostow todisti lauseen vuonna 1968. T\u00e4ydellinen hyperbolinen monisto voidaan samaistaa hyperbolisen avaruuden isometrioiden ryhm\u00e4n eli konformikuvausten M\u00f6bius-ryhm\u00e4n aliryhm\u00e4n kanssa. T\u00e4m\u00e4 aliryhm\u00e4 on isomor\ufb01nen moniston perusryhm\u00e4n kanssa. Monisto saadaan t\u00e4ll\u00f6in tekij\u00e4varuutena t\u00e4m\u00e4n aliryhm\u00e4n toiminnassa hyperbolisella avaruudella. Lause todistetaan osoittamalla, ett\u00e4 jos monistoja vastaavat aliryhm\u00e4t ovat kvasikonformikuvauksen konjugoimia, niin t\u00e4m\u00e4 kvasikonformikuvaus onkin konformikuvaus. M\u00f6bius-ryhm\u00e4 osoitetaan hyperbolisen avaruuden isometrioiden ryhm\u00e4ksi k\u00e4ytt\u00e4en apuna sen isomor\ufb01suutta ryhm\u00e4n O(1,n + 1) kanssa. Osoitetaan my\u00f6s, ett\u00e4 hyperbolinen avaruus on jokaisen hyperbolisen moniston isometrinen peite. Kuoren eli yleistetyn annuluksen konformikapasiteetin jatkuvuus todistetaan aiempien aputulosten avulla. Topologisen ryhm\u00e5n operaatiossa invarianttia Haarin mittaa k\u00e4ytt\u00e4en todistetaan er\u00e4s p\u00e4\u00e4lauseen todistuksessa tarvittava apulause. P\u00e4\u00e4lause todistetaan k\u00e4ytt\u00e4en lis\u00e4ksi konformikapasiteetin jatkuvuutta, polaarihajotelmaa, kvasikonformikuvauksen jatkumista pallon reunalle ja sit\u00e4, ett\u00e4 1-kvasikonformikuvaus on konformikuvaus.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2018-08-08T06:41:15Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2018-08-08T06:41:15Z (GMT). No. of bitstreams: 0\n Previous issue date: 2018", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "39", "language": "", "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": "fin", "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": "topologiset ryhm\u00e4t", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "kvasikonformikuvaukset", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "hyperbolinen geometria", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Mostow'n rigiditeettilause", "language": "", "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-201808083785", "language": "", "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": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "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": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "monistot", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "geometria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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