Rigidity of length functions over strata of flat metrics

Fu, Ser-Wei

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

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

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

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

Copyright and License Information

Copyright 2014 Ser-Wei Fu

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