Rigidity of length functions over strata of flat metrics

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Fu, Ser-Wei

Contributors dc:contributor

• Leininger, Christopher J.
• Kapovitch, Ilia
• Athreya, Jayadev S.
• Dowdall, Spencer

• Surface
• Quadratic differential
• Measured foliation
• Train track

Statement dc:rights

• Copyright 2014 Ser-Wei Fu

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/49531