On the set of complex points of a 2-sphere

TL;DR

This paper investigates the structure of complex points on a 2-sphere embedded in the boundary of a strictly pseudoconvex domain in a72, analyzing how smoothness affects the set of complex points.

Contribution

It provides a detailed analysis of the dependence of the set of complex points on the smoothness of the embedded 2-sphere in a pseudoconvex domain boundary.

Findings

The structure of complex points varies with the smoothness of the embedded sphere.

Smoothness conditions influence the size and nature of the set of complex points.

Results contribute to understanding CR geometry and complex analysis in several variables.

Abstract

Let $G$ be a strictly pseudoconvex domain in $\mathbb{C}^2$ with $C^\infty$-smooth boundary $\partial G$. Let $S$ be a 2-dimensional sphere embedded into $\partial G$. Denote by $\mathcal{E}$ the set of all complex points on $S$. We study how the structure of the set $\mathcal{E}$ depends on the smoothness of $S$