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 $C^2$. 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.