A Better Lower Bound Estimation of Brennan's Conjecture

TL;DR

This paper presents new equivalent formulations and lower bound estimates for Brennan's conjecture, including one involving Schwarzian derivatives, and verifies the conjecture in specific cases.

Contribution

It introduces an equivalent proposition of Brennan's conjecture and provides new lower bound estimates, one linked to Schwarzian derivatives, with partial verification.

Findings

Established an equivalent proposition of Brennan's conjecture.

Proposed two lower bound estimates, one involving Schwarzian derivatives.

Verified the conjecture in certain special conditions.

Abstract

In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the conjecture in some special conditions.