Mathematics > Complex Variables
[Submitted on 5 Apr 2022]
Title:Lelong Numbers of $m$-Subharmonic Functions Along Submanifolds
View PDFAbstract:We study the possible singularities of an $m$-subharmonic function $\varphi$ along a complex submanifold $V$ of a compact Kähler manifold, finding a maximal rate of growth for $\varphi$ which depends only on $m$ and $k$, the codimension of $V$. When $k < m$, we show that $\varphi$ 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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