2026-09-20T21:36:30Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/115382 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Dunfield, Nathan Albin, Pierre Hirani, Anil Samperton, Eric 2022-05 application/pdf en text 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 Stable isoperimetric ratios and hyperbolic geometry Rudd, Cameron Gates 2022-04-19 hyperbolic geometry 3-manifolds low-dimensional topology geometric topology geometric analysis spectral geometry 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. Thesis eng https://hdl.handle.net/2142/115382 © 2022 Cameron Gates Rudd Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics