Bers isomorphism on the universal Teichmüller curve (Q2466806)

The author explicitly describes the Bers isomorphism \(\mathfrak{B}\) between the universal Teichmüller curve \(F(1)\) (which involves quasi-symmetric homeomorphisms of the circle) and the Teichmüller space \(T(\Gamma_0)\) of the cyclic group \(\Gamma_0\) generated by \(z\mapsto z+1\) (which involves bounded Beltrami differentials on the unit disc). He then computes the derivative of \(\mathfrak{B}\) and shows that the pull-back of the Velling-Kirillov metric from \(F(1)\) to \(T(\Gamma_0)\) is \(2\pi/3\) times the natural right-invariant extension to \(T(\Gamma_0)\) of the Takhtajan-Zograf metric. The paper is clearly written and the computations are explicit.