An Analytic Disc Approach to the Notion of Type of Points

Author

Roman Dwilewicz, Missouri University of Science and TechnologyFollow
C. Denson Hill

Abstract

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.

Recommended Citation

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 https://doi.org/10.1512/iumj.1992.41.41038

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

0022-2518

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1992 Indiana University Mathematics Journal, All rights reserved.

Publication Date

01 Jan 1992