Marked length spectrum rigidity from rigidity on subsets
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.
Keywords
Cite
@article{arxiv.2304.13209,
title = {Marked length spectrum rigidity from rigidity on subsets},
author = {Stephen Cantrell and Eduardo Reyes},
journal= {arXiv preprint arXiv:2304.13209},
year = {2024}
}
Comments
26 pages (Version 2 is significantly different from Version 1: the final two sections and results regarding approximate rigidity have been removed from V1. These results will appear in a different work. New results and applications have also been added to V2.)