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Thurston's asymmetric metrics for Anosov representations

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arxiv 2210.05292 v2 pith:6LT4KN6C submitted 2022-10-11 math.DG math.DSmath.GT

León Carvajales , Xian Dai , Beatrice Pozzetti , Anna Wienhard This is my paper · ORCID
classification math.DGmath.DSmath.GT
keywords asymmetricfinslerrepresentationsanosovassociatedcasesnormspace
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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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  1. Maximal stretch and Lipschitz maps on Riemannian manifolds of negative curvature

    math.DG 2025-07 conditional novelty 8.0 of 10

    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.

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