The trace operator of quasi-plurisubharmonic functions on compact K\"ahler manifolds
Differential Geometry
2026-03-16 v2 Complex Variables
Abstract
We introduce the trace operator for quasi-plurisubharmonic functions on compact K\"ahler manifolds, allowing to study the singularities of such functions along submanifolds where their generic Lelong numbers vanish. Using this construction we obtain novel extension theorems and give applications to restricted volumes of big line bundles.
Keywords
Cite
@article{arxiv.2403.08259,
title = {The trace operator of quasi-plurisubharmonic functions on compact K\"ahler manifolds},
author = {Tamás Darvas and Mingchen Xia},
journal= {arXiv preprint arXiv:2403.08259},
year = {2026}
}
Comments
v.1 comments welcome v.2 accepted version