A volume stability theorem on toric manifolds with positive Ricci curvature

In this short note, we will prove a volume stability theorem which says that if an n-dimensional toric manifold $M$ admits a ${\mathbb{T}}^n$ invariant K"ahler metric $\omega$ with Ricci curvature no less than 1 and its volume is close to the volume of ${\mathbb{C}\mathbb{P}}^n$, $M$ is bi-holomorphic to ${\mathbb{C}\mathbb{P}}^n$.