2026-09-21T14:42:57Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/49531 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Leininger, Christopher J. Kapovitch, Ilia Leininger, Christopher J. Athreya, Jayadev S. Dowdall, Spencer Fu, Ser-Wei 2014-05-30T16:48:39Z 2014-05-30T16:48:39Z 2014-05 2014-05-30T16:48:39Z 2014-05 In this thesis we consider strata of flat metrics coming from quadratic differentials (semi-translation structures) on surfaces of finite type. We provide a necessary and sufficient condition for a set of simple closed curves to be spectrally rigid over a stratum with enough complexity, extending a result of Duchin-Leininger-Rafi. Specifically, for any stratum with more unmarked zeroes than the genus, the Sigma-length-spectrum of a set of simple closed curves Sigma determines the flat metric in the stratum if and only if Sigma is dense in the projective measured foliation space. We also prove that flat metrics in any stratum are locally determined by the Sigma-length-spectrum of a finite set of closed curves Sigma. Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-04-23T13:07:33Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 3 Fu_Ser-Wei.tex: 145067 bytes, checksum: 7d8220ea0ca31f78dc1d21bf217f1972 (MD5) Fu_Sew-Wei.pdf: 471225 bytes, checksum: f1d3bbd89804447a0624c4e66ec4ce17 (MD5) Fu_Ser-Wei.pdf: 471225 bytes, checksum: f1d3bbd89804447a0624c4e66ec4ce17 (MD5) Made available in DSpace on 2014-05-30T16:48:39Z (GMT). No. of bitstreams: 3 Ser-Wei_Fu.pdf: 471396 bytes, checksum: f52dde3916c4af9400c459636e0eb4b9 (MD5) Fu_Ser-Wei.tex: 145109 bytes, checksum: c8717eff0153ecb63b0a14024c0dbcc3 (MD5) license.txt: 4056 bytes, checksum: 050d47a411c9a384911554170543df88 (MD5) http://hdl.handle.net/2142/49531 en Copyright 2014 Ser-Wei Fu Surface Quadratic differential Measured foliation Train track Rigidity of length functions over strata of flat metrics text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD