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Haken, Wolfgang Callahan, Patrick James 2011-05-07T13:58:19Z 2011-05-07T13:58:19Z 1994 This thesis uses techniques from spectral geometry and builds from the work of Schoen, Culler and Shalen, Meyerhoff, and others to obtain various estimates and inequalities involving geometric data of hyperbolic 3-manifolds. These give numerical relationships between quantities like volume, length of geodesics, area of embedded surfaces, isoperimetric constants, eigenvalues of the Laplacian, and Margulis numbers for hyperbolic 3-manifolds. Made available in DSpace on 2011-05-07T13:58:19Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9503152.pdf: 1011703 bytes, checksum: e0f9fd9b79b7fd2b3148531e56fc2d3a (MD5) Previous issue date: 1994 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:01:26Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:29:08-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission Open Restriction set for Item 23127 on 2020-07-10T17:46:07Z with date null by lac7@illinois.edu. Open Restriction set for Item 23127 on 2020-07-10T17:46:10Z with date null by lac7@illinois.edu. Open AAI9503152 (UMI)AAI9503152 http://hdl.handle.net/2142/22992 eng Copyright 1994 Callahan, Patrick James Mathematics Spectral geometry of hyperbolic 3-manifolds text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.