On a Holomorphic Family of Stein Manifolds with Strongly Pseudoconvex Boundaries

Xiaoshan Li,Guicong Su

doi:10.1007/s12220-019-00160-z

Abstract

We study the stable embedding problem for a CR family of 3-dimensional strongly pseudoconvex CR manifolds with each fiber bounding a stein manifold.

Highlights

Let X be a compact strongly pseudoconvex CR manifold
The question of whether or not X admits a CR embedding into a complex Euclidean space has attracted a lot attention. This amounts to showing that the manifold has a sufficiently rich collection of global CR functions
There are examples [5,14,28] which show that even when the CR structure on X is locally embeddable, it can happen that the global CR functions on X fail to separate points of X

Summary

Introduction

Let X be a compact strongly pseudoconvex CR manifold. Definition 1.3 Let = {t ∈ C : |t| < 1} be the unit disk in the complex plane C and {Xt }t∈ be a parameterized family of compact strongly pseudoconvex CR manifolds of real dimension 2n − 1. Problem 1.4 ( [19]) Let {Xt }t∈ be a CR family of 3-dimensional strongly pseudoconvex CR manifold.

Results

Conclusion