Marked length spectral rigidity for flat metrics

Anja Bankovic; Christopher J. Leininger

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arXiv · 1504.01159

Marked length spectral rigidity for flat metrics

Anja Bankovic·Christopher J. Leininger

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Abstract

In this paper we prove that the space of flat metrics (nonpositively curved Euclidean cone metrics) on a closed, oriented surface is marked length spectrally rigid. In other words, two flat metrics assigning the same lengths to all closed curves differ by an isometry isotopic to the identity. The novel proof suggests a stronger rigidity result for flat metrics.

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BibTeX RIS

Anja Bankovic, Christopher J. Leininger. 2015-04-05. Marked length spectral rigidity for flat metrics. https://arxiv.org/abs/1504.01159

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