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arXiv · 2403.08259

The trace operator of quasi-plurisubharmonic functions on compact K\"ahler manifolds

Tamás Darvas·Mingchen Xia
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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 $L^2$ extension theorems and give applications to restricted volumes of big line bundles.

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Tamás Darvas, Mingchen Xia. 2024-03-13. The trace operator of quasi-plurisubharmonic functions on compact K\"ahler manifolds. https://arxiv.org/abs/2403.08259

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