The trace operator of quasi-plurisubharmonic functions on compact Kähler manifolds

Abstract

We introduce the trace operator for quasi-plurisubharmonic functions on compact Kähler manifolds, allowing to study the singularities of such functions along submanifolds where their generic Lelong numbers vanish. Using this construction we obtain novel $L^2$ extension theorems and give applications to restricted volumes of big line bundles.

v.1 comments welcome v.2 accepted version