University of Illinois Urbana-Champaign

Rigidity of length functions over strata of flat metrics

Fu, Ser-Wei

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Ser-Wei_Fu.pdf

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https://hdl.handle.net/2142/49531

Description

Title
Rigidity of length functions over strata of flat metrics
Author(s)
Fu, Ser-Wei
Issue Date
2014-05-30T16:48:39Z
Director of Research (if dissertation) or Advisor (if thesis)
Leininger, Christopher J.
Doctoral Committee Chair(s)
Kapovitch, Ilia
Committee Member(s)
  • Leininger, Christopher J.
  • Athreya, Jayadev S.
  • Dowdall, Spencer
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2014-05-30T16:48:39Z
Keyword(s)
  • Surface
  • 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.
Graduation Semester
2014-05
Permalink
http://hdl.handle.net/2142/49531
Copyright and License Information
Copyright 2014 Ser-Wei Fu

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