{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/45475"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/45475","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Length functions in flat metrics","abstract":"This dissertation is concerned with equivalence relations on homotopy classes of curves coming from various spaces of at metrics on a genus g >1 surface. We prove an analog of a result of Randol (building on work of Horowitz) for subfamilies of at metrics coming from q-di erentials. In addition we also describe how these equivalence relations are related to each other.","abstract_html":"This dissertation is concerned with equivalence relations on homotopy classes of curves coming from various spaces of at metrics on a genus g &gt;1 surface. We prove an analog of a result of Randol (building on work of Horowitz) for subfamilies of at metrics coming from q-di erentials. In addition we also describe how these equivalence relations are related to each other.","abstract_has_math":false,"creators":["Bankovic, Anja"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Leininger, Christopher J.","Athreya, Jayadev S.","Kapovitch, Ilia","Alexander, Stephanie B."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-08-22T16:41:19Z","date_published":"2013-08-22T16:41:19Z","updated_at":"2026-07-22T22:25:36Z","subjects":["hyperbolic metric","length functions","Euclidean cone metric","curves on surfaces"],"languages":["en"],"rights":["Copyright 2013 by Anja Bankovic. All rights reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/45475","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Leininger, Christopher J.","Athreya, Jayadev S.","Kapovitch, Ilia","Alexander, Stephanie B."]},{"key":"dc:creator","label":"Author","values":["Bankovic, Anja"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-08-22T16:41:19Z","2013-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["hyperbolic metric","length functions","Euclidean cone metric","curves on surfaces"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2013 by Anja Bankovic. All rights reserved."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/45475"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This dissertation is concerned with equivalence relations on homotopy classes of curves coming from various spaces of at metrics on a genus g >1 surface. We prove an analog of a result of Randol (building on work of Horowitz) for subfamilies of at metrics coming from q-di erentials. In addition we also describe how these equivalence relations are related to each other.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-07-02T13:37:39Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 thesis.tex: 72862 bytes, checksum: c1b7d18b76ebf65877666869ea3d01fb (MD5) Bankovic_Anja.pdf: 358494 bytes, checksum: ca839a66379629aa8805821afe14c919 (MD5)","Made available in DSpace on 2013-08-22T16:41:19Z (GMT). No. of bitstreams: 3 Anja_Bankovic.pdf: 358493 bytes, checksum: f77762bbcc0fd0e1a0f13274e29b9fd5 (MD5) thesis.tex: 72913 bytes, checksum: a96e41802162c3723a0e6cc05410c7ec (MD5) license.txt: 4063 bytes, checksum: 3d0f1323802024baa2937131bd2a8d6c (MD5)"]},{"key":"dc:title","label":"Title","values":["Length functions in flat metrics"]}]}],"canonical_facts":{"dc:contributor":["Leininger, Christopher J.","Athreya, Jayadev S.","Kapovitch, Ilia","Alexander, Stephanie B."],"dc:creator":["Bankovic, Anja"],"dc:date":["2013-08-22T16:41:19Z","2013-08"],"dc:description":["This dissertation is concerned with equivalence relations on homotopy classes of curves coming from various spaces of at metrics on a genus g >1 surface. We prove an analog of a result of Randol (building on work of Horowitz) for subfamilies of at metrics coming from q-di erentials. In addition we also describe how these equivalence relations are related to each other.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-07-02T13:37:39Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 thesis.tex: 72862 bytes, checksum: c1b7d18b76ebf65877666869ea3d01fb (MD5) Bankovic_Anja.pdf: 358494 bytes, checksum: ca839a66379629aa8805821afe14c919 (MD5)","Made available in DSpace on 2013-08-22T16:41:19Z (GMT). No. of bitstreams: 3 Anja_Bankovic.pdf: 358493 bytes, checksum: f77762bbcc0fd0e1a0f13274e29b9fd5 (MD5) thesis.tex: 72913 bytes, checksum: a96e41802162c3723a0e6cc05410c7ec (MD5) license.txt: 4063 bytes, checksum: 3d0f1323802024baa2937131bd2a8d6c (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/45475"],"dc:language":["en"],"dc:rights":["Copyright 2013 by Anja Bankovic. All rights reserved."],"dc:subject":["hyperbolic metric","length functions","Euclidean cone metric","curves on surfaces"],"dc:title":["Length functions in flat metrics"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:36Z"}