{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/121393"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/121393","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Quasiconformal mappings and fractal geometry","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","abstract_has_math":false,"creators":["Chrontsios Garitsis, Efstathios Konstantinos"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Hinkkanen, Aimo","Tyson, Jeremy","Erdogan, Burak","Hildebrand, AJ"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-08","date_published":"2023-08","updated_at":"2026-07-22T22:24:57Z","subjects":["Quasiconformal","Fractal","Geometry","Analysis"],"languages":["en","eng"],"rights":["Copyright 2023 Efstathios Konstantinos Chrontsios Garitsis"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/121393","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hinkkanen, Aimo","Tyson, Jeremy","Erdogan, Burak","Hildebrand, AJ"]},{"key":"dc:creator","label":"Author","values":["Chrontsios Garitsis, Efstathios Konstantinos"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-08","2023-05-04"]},{"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":["Quasiconformal","Fractal","Geometry","Analysis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2023 Efstathios Konstantinos Chrontsios Garitsis"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/121393"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","The student, Efstathios Konstantinos Chrontsios Garitsis, accepted the attached license on 2023-04-30 at 21:10.","The student, Efstathios Konstantinos Chrontsios Garitsis, submitted this Dissertation for approval on 2023-04-30 at 21:16.","This Dissertation was approved for publication on 2023-05-04 at 17:09.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19268 on 2023-12-04 at 16:59:37","This thesis discusses three different projects regarding fractals and quasiconformal mappings. The first project involves certain fractal Fourier series motivated by exponential sums studied in areas of number theory. We showed with Hildebrand that if for a function $f:\\N\\rightarrow \\C$ the sum $|\\sum_{n\\leq x}f(n)e^{2\\pi i n t}|$ grows at a specific uniform rate, then the Fourier series $\\sum_{n=1}^\\infty \\frac{f(n)}{n}e^{2\\pi i n t}$ is H\\\"older continuous, which provides upper bounds on the box-counting dimension of fractal sets associated with the series. The second project investigates the quasiconformal distortion of certain dimension notions and spectra. More specifically, we showed with Tyson that a quasiconformal map between domains in Euclidean spaces cannot change the dimensions of sets uncontrollably. This was previously known for the Hausdorff and box-counting dimensions, but our result applies on the Assouad dimension and spectrum, with the latter being the first result of its kind. The third project is motivated by the geometric definition of quasiconformality on the complex plane and provides interesting properties for certain quadrilaterals. Namely, we showed with Hinkkanen that every quadrilateral $Q$ of modulus in some interval $[1/K,K]$, $K>1$, needs to contain a disk of radius comparable to the maximum of the internal distances of $Q$, where the comparability constant only depends on $K$."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Quasiconformal mappings and fractal geometry"]}]}],"canonical_facts":{"dc:contributor":["Hinkkanen, Aimo","Tyson, Jeremy","Erdogan, Burak","Hildebrand, AJ"],"dc:creator":["Chrontsios Garitsis, Efstathios Konstantinos"],"dc:date":["2023-08","2023-05-04"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","The student, Efstathios Konstantinos Chrontsios Garitsis, accepted the attached license on 2023-04-30 at 21:10.","The student, Efstathios Konstantinos Chrontsios Garitsis, submitted this Dissertation for approval on 2023-04-30 at 21:16.","This Dissertation was approved for publication on 2023-05-04 at 17:09.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19268 on 2023-12-04 at 16:59:37","This thesis discusses three different projects regarding fractals and quasiconformal mappings. The first project involves certain fractal Fourier series motivated by exponential sums studied in areas of number theory. We showed with Hildebrand that if for a function $f:\\N\\rightarrow \\C$ the sum $|\\sum_{n\\leq x}f(n)e^{2\\pi i n t}|$ grows at a specific uniform rate, then the Fourier series $\\sum_{n=1}^\\infty \\frac{f(n)}{n}e^{2\\pi i n t}$ is H\\\"older continuous, which provides upper bounds on the box-counting dimension of fractal sets associated with the series. The second project investigates the quasiconformal distortion of certain dimension notions and spectra. More specifically, we showed with Tyson that a quasiconformal map between domains in Euclidean spaces cannot change the dimensions of sets uncontrollably. This was previously known for the Hausdorff and box-counting dimensions, but our result applies on the Assouad dimension and spectrum, with the latter being the first result of its kind. The third project is motivated by the geometric definition of quasiconformality on the complex plane and provides interesting properties for certain quadrilaterals. Namely, we showed with Hinkkanen that every quadrilateral $Q$ of modulus in some interval $[1/K,K]$, $K>1$, needs to contain a disk of radius comparable to the maximum of the internal distances of $Q$, where the comparability constant only depends on $K$."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/121393"],"dc:language":["en","eng"],"dc:rights":["Copyright 2023 Efstathios Konstantinos Chrontsios Garitsis"],"dc:subject":["Quasiconformal","Fractal","Geometry","Analysis"],"dc:title":["Quasiconformal mappings and fractal geometry"],"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":"2026-07-22T22:24:57Z"}