Plurisubharmonicity of the Dirichlet energy and deformations of polarized manifolds

Abstract

We show that if $\{M_t{\}}_{t\in \Delta }$ is a polarized family of compact Kähler manifolds over the open unit disk $\Delta$, if $N$ is a Riemannian manifold of nonpositive complexified sectional curvature, and if $\{{\varphi }_t:M_t\to N{\}}_{t\in \Delta }$ is a smooth family of pluriharmonic maps, then the Dirichlet energy $E({\varphi }_t)$ is a subharmonic function of $t\in \Delta$.

Supersedes arXiv:2004.13592