{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/115382"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/115382","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stable isoperimetric ratios and hyperbolic geometry","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms","abstract_has_math":false,"creators":["Rudd, Cameron Gates"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Dunfield, Nathan","Albin, Pierre","Hirani, Anil","Samperton, Eric"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-05","date_published":"2022-05","updated_at":"2026-07-22T22:24:54Z","subjects":["hyperbolic geometry","3-manifolds","low-dimensional topology","geometric topology","geometric analysis","spectral geometry"],"languages":["en","eng"],"rights":["© 2022 Cameron Gates Rudd"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/115382","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dunfield, Nathan","Albin, Pierre","Hirani, Anil","Samperton, Eric"]},{"key":"dc:creator","label":"Author","values":["Rudd, Cameron Gates"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-05","2022-04-19"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"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 geometry","3-manifolds","low-dimensional topology","geometric topology","geometric analysis","spectral geometry"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["© 2022 Cameron Gates Rudd"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/115382"]}]},{"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 2022-11-11 without embargo terms","The student, Cameron Rudd, accepted the attached license on 2022-04-06 at 14:59.","The student, Cameron Rudd, submitted this Dissertation for approval on 2022-04-06 at 15:04.","This Dissertation was approved for publication on 2022-04-19 at 13:31.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17599 on 2022-11-11 at 13:04:53","We show that for a closed hyperbolic 3-manifold, the size of the first eigenvalue of the Hodge Laplacian acting on coexact 1-forms is comparable to an isoperimetric ratio relating geodesic length and stable commutator length with comparison constants that depend polynomially on the volume and on a lower bound on injectivity radius, refining estimates of Lipnowski and Stern. We use this estimate to show that there exist sequences of closed hyperbolic 3- manifolds with injectivity radius bounded below and volume going to infinity for which the 1-form Laplacian has spectral gap vanishing exponentially fast in the volume."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Stable isoperimetric ratios and hyperbolic geometry"]}]}],"canonical_facts":{"dc:contributor":["Dunfield, Nathan","Albin, Pierre","Hirani, Anil","Samperton, Eric"],"dc:creator":["Rudd, Cameron Gates"],"dc:date":["2022-05","2022-04-19"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms","The student, Cameron Rudd, accepted the attached license on 2022-04-06 at 14:59.","The student, Cameron Rudd, submitted this Dissertation for approval on 2022-04-06 at 15:04.","This Dissertation was approved for publication on 2022-04-19 at 13:31.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17599 on 2022-11-11 at 13:04:53","We show that for a closed hyperbolic 3-manifold, the size of the first eigenvalue of the Hodge Laplacian acting on coexact 1-forms is comparable to an isoperimetric ratio relating geodesic length and stable commutator length with comparison constants that depend polynomially on the volume and on a lower bound on injectivity radius, refining estimates of Lipnowski and Stern. We use this estimate to show that there exist sequences of closed hyperbolic 3- manifolds with injectivity radius bounded below and volume going to infinity for which the 1-form Laplacian has spectral gap vanishing exponentially fast in the volume."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/115382"],"dc:language":["en","eng"],"dc:rights":["© 2022 Cameron Gates Rudd"],"dc:subject":["hyperbolic geometry","3-manifolds","low-dimensional topology","geometric topology","geometric analysis","spectral geometry"],"dc:title":["Stable isoperimetric ratios and hyperbolic geometry"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:54Z"}