Plurisubharmonicity and geodesic convexity of energy function on Teichmüller space

Inkang Kim, Xueyuan Wan, Genkai Zhang

Let $π:\mc{X}\to \mc{T}$ be Teichmüller curve over Teichmüller space $\mc{T}$, such that the fiber $\mc{X}_z=π^{-1}(z)$ is exactly the Riemann surface given by the complex structur…