Marked length spectrum rigidity from rigidity on subsets

2023/04/26 by Cantrell, Stephen, Reyes, Eduardo · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2304.13209

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 Teichmüller space equipped with a symmetrized version of the Thurston metric.

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