Quantization analysis of Moser-Trudinger equations in the Poincaré disk and applications

In this paper, we first establish the quantitative properties for positive solutions to the Moser-Trudinger equation in the two-dimensional Poincaré disk $\mathbb{B}^2$: \begin{equation*}\label{mt1} \left\{ \begin{aligned} &-Δ_{\mathbb{B}^2}u=λue^{u^2},\ x\in\mathbb{B}^2, &u\to0,\ \text{when