$L^2$ estimates for the $\bar{\partial }$ operator

Abstract

This is a survey article about $L^2$ estimates for the $\bar{\partial }$ operator. After a review of the basic approach that has come to be called the "Bochner-Kodaira Technique", the focus is on twisted techniques and their applications to estimates for $\bar{\partial }$, to $L^2$ extension theorems, and to other problems in complex analysis and geometry, including invariant metric estimates and the $\bar{\partial }$-Neumann Problem.

To appear in Bulletin of Mathematical Sciences