Hartogs' Extension Theorem

< Back to Projects

A Study of Holomorphic Functions in Several Complex Variables

This research explores Hartogs' Extension Theorem, a fundamental result in the theory of several complex variables that demonstrates significant differences between functions of one and multiple complex variables.

View the Full Paper

You can view the full paper below or download it directly.

Abstract

This paper examines Hartogs' Extension Theorem, which states that holomorphic functions defined on a domain with a hole can be analytically continued to the entire domain when dealing with functions of two or more complex variables. This contrasts with single-variable complex analysis, where holomorphic functions can have isolated singularities. We explore the proof of this theorem and its implications for complex analysis.