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math.GT2026
Flippered hyperbolic surfaces and renormalized volumes of their moduli spaces I
Yi Huang, Ivan Telpukhovskiy
We introduce a natural class of hyperbolic surfaces called flippered surfaces that generalize crowned hyperbolic surfaces (i.e.: worldsheets for open strings). We develop their Tei…
math.GT2025
Moduli spaces of open strings have polylogarithmic Mirzakhani volumes
Yi Huang, Ivan Telpukhovskiy
We show that the Mirzakhani volume, as introduced by Chekhov, of the moduli space of every crowned hyperbolic surface is naturally expressible as a sum of Gaussian rational multipl…
math.GT2019
Masur's criterion does not hold in the Thurston metric
Ivan Telpukhovskiy
We construct a counterexample for an analogue of Masur's criterion in the setting of Teichmüller space equipped with the Thurston metric. For that, we find a minimal, filling, non-…