Quantitative marked length spectrum rigidity for surfaces

2025/09/20 by Karen Butt, Butt, Karen
Engineering · #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Manufacturing Process and Optimization

paper · pdf · doi:10.48550/arxiv.2509.16829

openalex publication_date 2025/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a closed negatively curved surface (M, g) with marked length spectrum sufficiently close (multiplicatively) to that of a hyperbolic metric g₀ on M. We show there is a smooth diffeomorphism F:M → M with derivative bounds close to 1, depending on the ratio of the two marked length spectrum functions. This is a two-dimensional version of our main result in [But25b].

Citations

• Approximate marked length spectrum rigidity in coarse geometry
• Marked length spectrum rigidity for Anosov surfaces
• Approximate control of the marked length spectrum by short geodesics
• The marked length spectrum of Anosov manifolds
• Minimal stretch maps between hyperbolic surfaces
• Cocycles, symplectic structures and intersection

Related

• Quantitative marked length spectrum rigidity
• Rigidity of length-angle spectrum for closed hyperbolic surfaces
• A counterexample to marked length spectrum semi-rigidity
• Length spectral rigidity of non-positively curved surfaces
• Marked Length Spectrum Rigidity for Surface Amalgams