The complement of the closed unit ball in $\mathbb C^3$ is not subelliptic

TL;DR

This paper proves that the complement of the closed unit ball in complex three-dimensional space is not subelliptic, using a Hartogs extension theorem for holomorphic vector bundles to establish the result.

Contribution

It introduces a Hartogs type extension theorem for holomorphic vector bundles and applies it to demonstrate the non-subellipticity of the complement of the closed unit ball in  complex dimensions.

Findings

The complement of the closed unit ball in  is not subelliptic for n .

A new Hartogs type extension theorem for holomorphic vector bundles is established.

The result extends to all  for n .

Abstract

In this short note we show that $\mathbb C^n\setminus\bar{\mathbb B^n}$ is not subelliptic for $n \geq 3$. This is done by proving a Hartogs type extension theorem for holomorphic vector bundles bundles.