Degenerate complex Monge-Ampère equations with non-Kähler forms in bounded domains

2023/03/08 by Salouf, Mohammed
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.04897

Abstract

In this paper, we study weak solutions to complex Monge-Ampère equations of the form (ω+ dd^c φ)ⁿ= F(φ,.)dμ on a bounded strictly pseudoconvex domain in ℂⁿ, where ω is a smooth (1,1)-form, 0≤ F is a continuous non-decreasing function, and μ is a positive non-pluripolar measure. Our results extend previous works of Kołodziej and Nguyen \citeKN15,KN23a,KN23b who study bounded solutions, as well as Cegrell \citeCeg98,Ceg04,Ceg08, Czyż \citeCz09, Benelkourchi \citeBen09,Ben15 and others who treat the case when ω=0 and/or F=1.

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