A remark on finite type conditions

TL;DR

This paper demonstrates that a broad positivity condition, more general than pseudoconvexity, ensures the equality of regular and singular order of contact in specific cases when these numbers are four.

Contribution

It introduces a new positivity condition that generalizes pseudoconvexity and establishes its implications for contact order equality.

Findings

Positivity condition extends pseudoconvexity.

Regular and singular contact orders coincide at four.

Provides theoretical insight into contact order conditions.

Abstract

We prove that a certain positivity condition, considerably more general than pseudoconvexity, enables one to conclude that the regular order of contact and singular order of contact agree when these numbers are $4$.