On the extension of Kähler currents on compact complex manifolds

2026/08/02 by Jiafu Ning, Kai Pang, Haoyuan Sun +2
Mathematics · #math.CV

paper · pdf

9 pages, comments welcome

arxiv created 2026/08/02 · arxiv updated 2026/08/04

Abstract

Let (X,ω) be a compact Kähler manifold and let V⊂ X be a closed complex submanifold. Coman-Guedj-Zeriahi proposed the problem: is every ω|_V-plurisubharmonic function on V the restriction of an ω-plurisubharmonic function on X? In this paper, we solve this problem affirmatively, even for a compact Hermitian manifold.

Citations

• Transcendental Okounkov bodies
• On the extension of quasiplurisubharmonic functions
• On the extension of Kähler currents on compact Kähler manifolds: holomorphic retraction case
• On the extensions of Kähler currents on compact Kähler manifolds
• Extension of plurisubharmonic functions with growth control
• Numerical characterization of the Kähler cone of a compact Kähler manifold
• Pseudo-effective line bundles on compact Kähler manifolds