Marked length spectrum rigidity from rigidity on subsets

Stephen Cantrell; Eduardo Reyes

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arXiv · 2304.13209

Marked length spectrum rigidity from rigidity on subsets

Stephen Cantrell·Eduardo Reyes

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Abstract

We introduce a new method for studying length spectrum rigidity problems based on a combination of ideas from dynamical systems and geometric group theory. This allows us to compare the marked length spectrum of metrics and distance-like functions coming from various geometric origins. Using our new perspective, we provide concise proofs of well-known length spectrum rigidity results and are able to extend classical results to a variety of new settings. Our methods rely on studying Manhattan curves and a coarse geometric analogue of Teichm\"uller space equipped with a symmetrized version of the Thurston metric.

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Stephen Cantrell, Eduardo Reyes. 2023-04-26. Marked length spectrum rigidity from rigidity on subsets. https://arxiv.org/abs/2304.13209

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