# D'Angelo conjecture in the third gap interval

## TL;DR

This paper proves the D'Angelo conjecture for a specific class of rational holomorphic maps between unit balls, establishing degree bounds in the third gap interval for dimensions n ≥ 7.

## Contribution

It demonstrates that the degree of rational proper holomorphic maps from  to  in the third gap interval is at most 3, confirming the conjecture in this case.

## Key findings

- D'Angelo conjecture holds in the third gap interval.
- Degree of maps from  to  is at most 3 for n  7.
- Validates the conjecture for a broad class of rational maps.

## Abstract

We show the D'Angelo conjecture holds in the third gap interval. More precisely, we prove that the degree of any rational proper holomorphic map from $\mathbb{B}^n$ to $\mathbb{B}^{4n-6}$ with $n\geq 7$ is not more than $3$.