Domain of finite type

Summary

A domain of finite type is a domain in $\C^n$ with smooth boundary whose boundary has only finite order of contact with complex curves. The type, introduced by D'Angelo, measures how flat the boundary can be in complex directions. Strongly pseudoconvex domains have type $2$, while a boundary that contains a complex disc has infinite type. For pseudoconvex domains, finite type is the condition under which the $\bar\partial$-Neumann problem gains regularity, by work of Kohn and Catlin.