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.
R. Dwilewicz and C. D. Hill, "An Analytic Disc Approach to the Notion of Type of Points," Indiana University Mathematics Journal, Indiana University Mathematics Journal, Jan 1992.
The definitive version is available at http://dx.doi.org/10.1512/iumj.1992.41.41038
Mathematics and Statistics
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