Holomorphic Extension of CR Functions from Quadratic Cones

It is proved that CR functions on a quadratic cone M in ${\text{C}}^n$, 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 ${\text{C}}^2$ is also given.