English

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 L2L^2 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