Closed negatively curved manifolds have a Mather set of maximally stretched orbits that is nowhere dense unless the two metrics have proportional marked length spectra, in which case it is the whole unit tangent bundle.
Thurston's asymmetric metrics for Anosov representations
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abstract
We provide a good dynamical framework allowing to generalize Thurston's asymmetric metric and the associated Finsler norm from Teichm\"uller space to large classes of Anosov representations. In many cases, including the space of Hitchin representations, this gives a (possibly asymmetric) Finsler distance. In some cases we explicitly compute the associated Finsler norm.
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math.DG 1years
2025 1verdicts
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Maximal stretch and Lipschitz maps on Riemannian manifolds of negative curvature
Closed negatively curved manifolds have a Mather set of maximally stretched orbits that is nowhere dense unless the two metrics have proportional marked length spectra, in which case it is the whole unit tangent bundle.