A counterexample to marked length spectrum semi-rigidity

Andrey Gogolev; James Marshall Reber

A counterexample to marked length spectrum semi-rigidity

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arxiv 2309.10882 v2 pith:CCFKEH2D submitted 2023-09-19 math.DG math.DS

Andrey Gogolev , James Marshall Reber This is my paper · ORCID

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keywords closedprimebecomesconstructcontractscounterexamplecurveddiffeomorphism

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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 $f : (M,g^\prime) \rightarrow (M,g)$ which contracts every tangent vector.

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Rigidity of the hyperbolic marked energy spectrum and entropy for $k$-surfaces
math.DG 2024-12 conditional novelty 6.0 of 10

In negatively curved 3-manifolds, the marked p-energy spectrum and the modified energy entropy of k-surfaces are rigid: equality or asymptotic behavior forces the ambient curvature to be constant.

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