A Characterization of regular points by $L^2$ Extension Theorem
  In this article, we present that the germ of a complex analytic set at the origin in $\mathbb{C}^n$ is regular if and only if the related $L^2$ extension theorem holds. We also obtain a necessary condition of the $L^2$ extension of bounded holomorphic sections from singular analytic sets. 
Qi'an Guan, Zhenqian Li
math.CV