Work

Marked Length Spectrum Rigidity From Rigidity on Subsets

Year: 2025

Type: article

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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf351

Authors: Stephen Cantrell, Eduardo Reyes

Institutions: University of St Andrews, Pontificia Universidad Católica de Chile

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,534

OpenAlex ID: W4417089316