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Marked length spectrum rigidity from rigidity on subsets (2304.13209v2)
Published 26 Apr 2023 in math.GT and math.GR
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.