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Title:Rigidity of length functions over strata of flat metrics
Author(s):Fu, Ser-Wei
Director of Research:Leininger, Christopher J.
Doctoral Committee Chair(s):Kapovitch, Ilia
Doctoral Committee Member(s):Leininger, Christopher J.; Athreya, Jayadev S.; Dowdall, Spencer
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Quadratic differential
Measured foliation
Train track
Abstract: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.
Issue Date:2014-05-30
Rights Information:Copyright 2014 Ser-Wei Fu
Date Available in IDEALS:2014-05-30
Date Deposited:2014-05

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