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Stable isoperimetric ratios and hyperbolic geometry
Rudd, Cameron Gates
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RUDD-DISSERTATION-2022.pdf
RUDD-DISSERTATION-2022.pdf
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application/pdf
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- 2.48 MB
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https://hdl.handle.net/2142/115382
Description
- Title
- Stable isoperimetric ratios and hyperbolic geometry
- Author(s)
- Rudd, Cameron Gates
- Issue Date
- 2022-04-19
- Director of Research (if dissertation) or Advisor (if thesis)
- Dunfield, Nathan
- Doctoral Committee Chair(s)
- Albin, Pierre
- Committee Member(s)
- Hirani, Anil
- Samperton, Eric
- Department of Study
- Mathematics
- Discipline
- Mathematics
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Keyword(s)
- hyperbolic geometry, 3-manifolds, low-dimensional topology, geometric topology, geometric analysis, spectral geometry
- Abstract
- 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.
- Graduation Semester
- 2022-05
- Type of Resource
- Thesis
- Copyright and License Information
- © 2022 Cameron Gates Rudd
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Graduate Dissertations and Theses at Illinois PRIMARY
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