A counterexample to marked length spectrum semi-rigidity

Given a closed, orientable, negatively curved Riemannian surface (M,g) , we show how to construct a perturbation (M,g^{\prime}) such that each closed geodesic becomes longer, and yet there is no diffeomorphism {f \colon (M,g^\prime)\to (M,g)} which contracts every tangent vector.

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Publication Details

Journal
Groups Geometry and Dynamics
Published
2025-01-09
DOI
https://doi.org/10.4171/ggd/853
Primary Topic
Advanced Numerical Analysis Techniques
Type
article
Field-Weighted Citation Impact
0.00
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article

A counterexample to marked length spectrum semi-rigidity

James Marshall Reber, Andrey Gogolev
Groups Geometry and Dynamics
Advanced Numerical Analysis Techniques
article

A counterexample to marked length spectrum semi-rigidity

James Marshall Reber, Andrey Gogolev
article en

Abstract

Given a closed, orientable, negatively curved Riemannian surface (M,g) , we show how to construct a perturbation (M,g^{\prime}) such that each closed geodesic becomes longer, and yet there is no diffeomorphism {f \colon (M,g^\prime)\to (M,g)} which contracts every tangent vector.

Groups Geometry and Dynamics
The Ohio State University (US)
Openalex Percentile: Top 99%
Advanced Numerical Analysis Techniques
DOIOpen Access PDFOpenAlex
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A counterexample to marked length spectrum semi-rigidity — James Marshall Reber, Andrey Gogolev · Groups Geometry and Dynamics (2025) | TGRS Research Map | TGRS