Refined Large Deviation Principle for Branching Brownian Motion Conditioned to Have a Low Maximum

Conditioning a branching Brownian motion to have an atypically low maximum leads suppression of the mechanism. In this note, we consider conditioned below $\sqrt{2}\alpha t$ ($\alpha<1$). We study precise effects early/late first time and low/high location under condition. do so by imposing additional constraints on location. obtain large deviation estimates, as well optimal given constraints.