Smooth solutions to the complex Hessian equation

2012/02/11 by Lu Hoang Chinh, Chinh, Lu Hoang
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1202.2435

openalex publication_date 2012/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X,ω) be a compact Kähler manifold of dimension n, and fix 1≤ m≤ n. We prove that the complex Hessian equation (ω+dd^cφ)^m\wedge ω^n-m=fωⁿ, with 0

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