Monge-Ampère type equation on compact Hermitian manifolds

2023/11/25 by Li, Yinji, Lin, Genglong, Zhou, Xiangyu
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.14958

Abstract

Given a cohomology (1,1)-class \β\ of compact Hermitian manifold (X,ω) possessing a bounded potential and fixed a model potential ϕ, motivated by Darvas-Di Nezza-Lu and Li-Wang-Zhou's work, we show that degenerate complex Monge-Ampère equation (β+dd^c φ)ⁿ=e^λφμ has a unique solution in the relative full mass class E(X,β,ϕ), where μ is a non-pluripolar measure on X and λ≥0 is a fixed constant. As an application, we give an explicit description of Lelong numbers of elements in E(X,β,ϕ) which generalized a theorem of Darvas-Di Nezza-Lu in the Hermitian context.

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