Holomorphic Extension of CR Functions from Quadratic Cones

TL;DR

This paper establishes conditions under which CR functions on quadratic cones in complex space can be extended holomorphically from one side, generalizing minimality, and provides a classification of quadratic cones in two dimensions.

Contribution

It proves a criterion for one-sided holomorphic extension of CR functions on quadratic cones and offers a biholomorphic classification of these cones in c2b2.

Findings

CR functions extend holomorphically if no two-sided support exists

A geometric condition generalizing minimality is identified

A classification of quadratic cones in c2b2 is provided

Abstract

It is proved that CR functions on a quadratic cone M in $\C^n$, n>1, admit one-sided holomorphic extension if and only if M does not have two-sided support, a geometric condition on M which generalizes minimality in the sense of Tumanov. A biholomorphic classification of quadratic cones in $\C^2$ is also given.