Abstract

At each point of a smooth hypersurface in a complex Euclidean space, it is associated three regular types called regular contact types, commutator types and Levi types. Kohn showed that these three types are in fact the same for a hypersurface in C². In the case of complex dimension three or more, pseudoconvexity is needed and it has been conjectured that pseudoconvexity is sufficient for equivalence of these three types. We will survey recent progress on this conjecture, especially, my joint work with Yin on the solution in the case of complex dimension three.