Strongly pseudoconvex domain

Summary

A strongly pseudoconvex domain is a domain in $\C^n$ with $C^2$ boundary whose Levi form is positive definite at every boundary point. It is also called a strictly pseudoconvex domain. It is the complex analogue of a strictly convex domain. In this class the analysis of several complex variables works best. The $\bar\partial$-equation has good estimates, and every boundary point is locally convex after a holomorphic change of coordinates.