# The Diederich-Fornaess Index and Good Vector Fields

## TL;DR

This paper explores how certain geometric conditions on pseudoconvex domains ensure the equivalence of the Diederich-Fornaess Index to one, linking it to the existence of good vector fields for regularity of the Bergman Projection.

## Contribution

It establishes a new connection between the Diederich-Fornaess Index and good vector fields under specific geometric conditions on the domain.

## Key findings

- If the set of infinite type points is well-behaved, then the Diederich-Fornaess Index equals one.
- Existence of good vector fields implies the Diederich-Fornaess Index is one.
- Provides conditions under which regularity of the Bergman Projection is guaranteed.

## Abstract

We consider the relationship between two sufficient conditions for regularity of the Bergman Projection on smooth, bounded, pseudoconvex domains. We show that if the set of infinite type points is reasonably well-behaved, then the existence of a family of good vector fields in the sense of Boas and Straube implies that the Diederich-Fornaess Index of the domain is equal to one.