# Some remarks on polar sets to sums of squares

## TL;DR

This paper discusses the geometric conditions, specifically the nature of polar sets, that influence the hypoellipticity of certain differential operators, emphasizing the importance of the polar not being a spiral domain.

## Contribution

It introduces the geometric criterion involving polar sets as a necessary condition for hypoellipticity, highlighting the role of spiral domains.

## Key findings

- Polar sets not being spiral domains are necessary for hypoellipticity.
- Geometric properties of polar sets influence differential operator regularity.
- Provides insights into the structure of hypoelliptic operators.

## Abstract

We argue that a necessary condition for hypoellipticity is that the polar is not a spiral domain.