Hartogs extension for systems of differential equations

TL;DR

This paper investigates the conditions under which singularities in overdetermined systems of differential equations can be removed, emphasizing the importance of the characteristic variety's dimension in this process.

Contribution

It introduces a new perspective on removable singularities by linking them to the dimension of the characteristic variety in differential systems.

Findings

Dimension of the characteristic variety influences singularity removability.

Removable singularities are characterized by specific properties of the characteristic variety.

The study provides criteria for singularity removal based on geometric analysis.

Abstract

The phenomenon of removable singularity is studied for overedetermined systems of differential equations. We show that the dimension of the characteristic variety plays a key role in the problem.