# 博学堂讲座预告（第433讲）

Title：Convexity and Plurisubharmonicity of energy functional on Teichmuller space.

Abstract: We consider the energy functional $E(u)$ of harmonic maps$u: (M, g)\to S$ from a Riemannian manifold $M$ to a Riemann surface $S$ of genus $g$as well as harmonic maps $u: S\to M$. The energy $E(u)$can be defined as a function on the Teichmuller space $\mathcal T$of $S$ as the hyperbolic metric of $S$varies. We prove Weil-Petterson geodesic convexity and plurisubharmonicity of $E$ on $\mathcal T$. (Joint work with I. Kim and Xueyuan Wan.)

Genkai Zhang (Chalmers Univ. of Tech. and Gothenburg Univ., Sweden):