# On a Holomorphic Family of Stein Manifolds with Strongly Pseudoconvex Boundaries

## TL;DR

This paper investigates the stable embedding problem for a family of 3-dimensional strongly pseudoconvex CR manifolds, each bounding a Stein manifold, contributing to the understanding of complex structures and embeddings in several complex variables.

## Contribution

It introduces a new approach to the stable embedding problem for CR families with strongly pseudoconvex boundaries, expanding the theory of Stein manifolds and CR geometry.

## Key findings

- Established conditions for stable embeddings in CR families
- Demonstrated existence of Stein fillings for the CR manifolds
- Provided new insights into the structure of strongly pseudoconvex boundaries

## 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.