An Analytic Disc Approach to the Notion of Type of Points


The purpose of this paper is to give an analytic disc approach to the notion of type of points. We consider here the case of a real hypersurfaces M in C2; however, this approach with all of its consequences, can be generalized, with some modifications, to the case of arbitrary CR manifolds. This will be discussed in subsequent papers. In this paper we define a real valued function phi = phi(p,delta), p over M, delta over R : delta>0, which characterizes points of finite type (in this sense of Kohn, Bloom-Graham, D'Angelo), and more importantly, distinguishes between different kinds of points of infinite type (e.g. points where M is minimal in the sense of Tumanov). As a byproduct of the latter characterization, we get a very simple proof of the holomorphic extension of CR functions (result of Trepreau) which avoids all technical difficulties. As another application of the type function we get boundary estimates for plurisubharmonic functions.


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© 1992 Indiana University Mathematics Journal, All rights reserved.

Publication Date

01 Jan 1992