Titlel: The pressure metric on quasi-Fuchsian spaces
Abstract: Thermodynamic formalism, as initially developed by Bowen and Ruelle, can be used to quantify the difference between two Anosov flows in terms of a "pressure semi-norm" on suitable spaces of Hölder functions. McMullen showed that the Weil-Petersson metric on Teichmüller space can be interpreted in these terms, after which "pressure metrics" were defined on broader representation varieties, for instance on quasi-Fuchsian spaces by Bridgeman and on Hitchin components by Bridgeman, Canary, Labourie and Sambarino. While the infinitesimal structure at the Fuchsian locus is well-understood in these varieties, almost nothing is known on the global behaviour of pressure metrics. In joint work with Ursula Hamenstädt, Frieder Jäckel and Yongquan Zhang, we show that the pressure metric on quasi-Fuchsian spaces has finite diameter. As a curious consequence, the Fuchsian locus is highly distorted.
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