Degenerate complex Hessian equations with arbitrary measure in bounded domains

2025/04/11 by Van Phu, Nguyen, Hai, Le Mau
#32Q15 #32U05 #32W20 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.08592

Abstract

Let Ω be a bounded strictly m-pseudoconvex domain of ℂⁿ. We solve degenerate complex Hessian equations of the form (ω+ dd^c φ)^m\wedgeβ^n-m = μ in the generalized Cegrell classes K_m(Ω,ω,ϕ), where ϕ∈ E_m(Ω) is a m-maximal function, ω is a smooth real (1,1)-form defined in a neighborhood of Ω and μ is a positive Radon measure which is dominated by a Hessian measure of m-subharnomic functions in Cegrell class.

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