2021/05/18 by Jiafu Ning, Zhiwei Wang, Ning, Jiafu +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2105.08224
openalex publication_date 2021/05/18 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28
In the present paper, we show that given a compact Kähler manifold (X,ω) with a Kähler metric ω, and a complex submanifold V⊂ X of positive dimension, if V has a holomorphic retraction structure in X, then any quasi-plurisubharmonic function φ on V such that ω|V+√(-1)∂∂φ≥ εω|V with ε>0 can be extended to a quasi-plurisubharmonic function Φ on X, such that ω+√(-1)∂∂ Φ≥ ε'ω for some ε'>0. This is an improvement of results in \citeWZ20. Examples satisfying the assumption that there exists a holomorphic retraction structure contain product manifolds, thus contains many compact Kähler manifolds which are not necessarily projective.