Classification of solutions to the singular Liouville's equation associated with the $N$ Finsler Laplacian

In this paper, we classify a class of singular Liouville’s equation associated with the Finsler-$N$-Laplacian for any $\beta \in (0,N)$ \begin{align*} -$\mathrm{d}\mathrm{i}\mathrm{v}$\left(F^{N-1}(\nabla u)DF(\nabla u)\right)=\hat{F}^{o}(x)^{-β}e^u\ \ $\text{in }$ $\mathbb{R}$^{N}\backslash {0}, \end{align*} under the finite mass condition ${\int }_{{\mathbb{R}}^N}{\widehat{F}}^o(x{)}^{-\beta }{e}^{u}dx<+\mathrm{\infty }$. Here $F$ is a convex function, which is positively homogeneous of degree 1, and its polar $F^o$ represents a Finsler metric on ${\mathbb{R}}^N$, ${\widehat{F}}^o(x)=F^o(-x)$. Our result relaxes the mass condition required in the classification result in [39]