{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/72527"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/72527","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Approximable Quasidisks","abstract":"Here we provide a simple outline of the contents of this dissertation.","abstract_html":"Here we provide a simple outline of the contents of this dissertation.","abstract_has_math":false,"creators":["Koh, Ngin-Tee"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Miles, Joseph"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-17T23:17:40Z","date_published":"2014-12-17T23:17:40Z","updated_at":"2026-07-22T22:26:07Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI3362942"],"render_values":[{"text":"(UMI)AAI3362942","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/72527","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Miles, Joseph"]},{"key":"dc:creator","label":"Author","values":["Koh, Ngin-Tee"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-17T23:17:40Z","10000-01-01","2009"]},{"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":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/72527","(UMI)AAI3362942"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Here we provide a simple outline of the contents of this dissertation.","Chapter 1 gives a brief account of some developments in the theory of quasiconformal mappings as well as its important role in complex analysis and other branches of mathematics.","In Chapter 2, we introduce some basic concepts about the theory of quasiconformal mappings.","Chapter 3 lists some distortion theorems. Other estimates are derived as needed. Finally we apply these results to construct a quasiconformal reflection with bounded partial derivatives near the boundary.","Chapter 4 provides univalence and quasiconformal extension criteria for an arbitrary quasidisk.","In Chapter 5, we prove that a quasidisk with an analytic boundary is approximable. This technical undertaking involves several lemmas. The main idea is to construct a family of quasiconformal reflections whose partial derivatives converge uniformly near the boundary of the quasidisk. Our boundary assumptions, which make this possible, also allow for a choice of reflections which are anti-conformal in a neighborhood of the boundary. Without this last feature, which is crucial to establishing Proposition 5.7, it is unlikely that 2.2 in Definition 2.23 would be satisfied.","Made available in DSpace on 2014-12-17T23:17:40Z (GMT). No. of bitstreams: 1 3362942.pdf: 499265 bytes, checksum: a518505f072418624b33e6e83cad8ae7 (MD5) Previous issue date: 2009","Embargo set by: Seth Robbins for item 72695 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","53 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009."]},{"key":"dc:title","label":"Title","values":["Approximable Quasidisks"]}]}],"canonical_facts":{"dc:contributor":["Miles, Joseph"],"dc:creator":["Koh, Ngin-Tee"],"dc:date":["2014-12-17T23:17:40Z","10000-01-01","2009"],"dc:description":["Here we provide a simple outline of the contents of this dissertation.","Chapter 1 gives a brief account of some developments in the theory of quasiconformal mappings as well as its important role in complex analysis and other branches of mathematics.","In Chapter 2, we introduce some basic concepts about the theory of quasiconformal mappings.","Chapter 3 lists some distortion theorems. Other estimates are derived as needed. Finally we apply these results to construct a quasiconformal reflection with bounded partial derivatives near the boundary.","Chapter 4 provides univalence and quasiconformal extension criteria for an arbitrary quasidisk.","In Chapter 5, we prove that a quasidisk with an analytic boundary is approximable. This technical undertaking involves several lemmas. The main idea is to construct a family of quasiconformal reflections whose partial derivatives converge uniformly near the boundary of the quasidisk. Our boundary assumptions, which make this possible, also allow for a choice of reflections which are anti-conformal in a neighborhood of the boundary. Without this last feature, which is crucial to establishing Proposition 5.7, it is unlikely that 2.2 in Definition 2.23 would be satisfied.","Made available in DSpace on 2014-12-17T23:17:40Z (GMT). No. of bitstreams: 1 3362942.pdf: 499265 bytes, checksum: a518505f072418624b33e6e83cad8ae7 (MD5) Previous issue date: 2009","Embargo set by: Seth Robbins for item 72695 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","53 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009."],"dc:identifier":["http://hdl.handle.net/2142/72527","(UMI)AAI3362942"],"dc:subject":["Mathematics"],"dc:title":["Approximable Quasidisks"],"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":"2026-07-22T22:26:07Z"}