Plurisubharmonicity of the Dirichlet energy and deformations of polarized manifolds

2021/10/30 by Che-Hung Huang, Huang, Che-Hung
Mathematics · #Advanced Algebra and Geometry #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2111.00237

openalex publication_date 2021/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if \M_t\_{t∈ 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→ N\_{t∈ Δ} is a smooth family of pluriharmonic maps, then the Dirichlet energy E(ϕ_t) is a subharmonic function of t∈Δ.

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