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Title of Journal: Geom Dedicata

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Abbravation: Geometriae Dedicata

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Springer Netherlands

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DOI

10.1016/0167-2789(95)90063-2

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1572-9168

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Length spectra and strata of flat metrics

Authors: SerWei Fu
Publish Date: 2013/12/07
Volume: 173, Issue: 1, Pages: 281-298
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Abstract

In this paper we consider strata of flat metrics coming from quadratic differentials semitranslation 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 zeroes than the genus the Sigma lengthspectrum 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 lengthspectrum of a finite set of closed curves Sigma

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  16. Explicit computation of the Chern character forms
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