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arXiv · 2204.01963

Lelong Numbers of $m$-Subharmonic Functions Along Submanifolds

Jianchun Chu·Nicholas McCleerey
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Abstract

We study the possible singularities of an $m$-subharmonic function $φ$ along a complex submanifold $V$ of a compact Kähler manifold, finding a maximal rate of growth for $φ$ which depends only on $m$ and $k$, the codimension of $V$. When $k < m$, we show that $φ$ has at worst log poles along $V$, and that the strength of these poles is moveover constant along $V$. This can be thought of as an analogue of Siu's theorem.

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Jianchun Chu, Nicholas McCleerey. 2022-04-05. Lelong Numbers of $m$-Subharmonic Functions Along Submanifolds. https://arxiv.org/abs/2204.01963

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