I've heard it said that Teichmüller space gives a metric to the space of all metric spaces.
If this is so, where do the Lp spaces sit in the space of all metric spaces?
2026-02-23 02:37:19.1771814239
how do the Lp spaces sit inside Teichmüller space?
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What you heard said is wrong. Instead, the Teichmüller space of an oriented surface $S$ of finite type gives a metric to the space of (isotopy classes of) complete, finite area hyperbolic metrics on $S$, meaning Riemannian metrics of constant curvature $-1$.