Propagation of CR extendibility at the vertex of a complex sector

TL;DR

This paper investigates the conditions under which CR extendibility propagates at the vertex of a complex sector within a CR manifold, establishing a precise criterion involving the sector's angle and the manifold's vanishing order.

Contribution

It provides a necessary and sufficient condition for propagation of CR extendibility at a sector vertex based on geometric and analytic parameters.

Findings

Propagation occurs if and only if the angle exceeds the reciprocal of the vanishing order.

The criterion links geometric angle with analytic vanishing order.

The result clarifies the geometric conditions for CR extendibility in complex sectors.

Abstract

We study propagation of CR extendibility at the vertex $p$ of an analytic sector $A$ contained in a CR manifold $M$. Let $k$ be the weighted vanishing order of $M$ and $\alpha $ the complex angle of $A$ at $p$. Propagation takes place if and only if $\alpha>\frac1k$.