Plurisubharmonicity of the Dirichlet energy and deformations of polarized manifolds

Che-Hung Huang

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arXiv · 2111.00237

Plurisubharmonicity of the Dirichlet energy and deformations of polarized manifolds

Che-Hung Huang

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Abstract

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

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Che-Hung Huang. 2021-10-30. Plurisubharmonicity of the Dirichlet energy and deformations of polarized manifolds. https://arxiv.org/abs/2111.00237

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