chapter  4
24 Pages

Points of Finite Type

WithKranlz Steven.G

In case the hypersurface bounds a pseudoconvex domain of finite type, the measurements turn out to be biholomorphic invariants of the domain itself. The notion of finite type is “finitely determined.” A property is finitely determined when it depends on some finite Taylor polynomial of the defining function, but is independent of higher order terms. The class of domains with a positive definite defining form—that is, those for which there is a defining function without any negative squares— is a subclass for which many considerations in the general theory are easier. The original definition of point of finite type was restricted to domains in two dimensions. Kohn was seeking conditions for subelliptic estimates on pseudoconvex domains, and was led to the study of iterated commutators. The chapter shows that this condition and several others are all equivalent, in the special two-dimensional case.