The sharp volume gap for Kähler manifolds with positive Ricci curvature

Chi Li, Minghao Miao, Kewei Zhang

We prove a sharp volume gap estimate: if an $n$-dimensional compact Kähler manifold $(X,\omega )$ satisfies $\mathrm{Ric}(\omega )\ge (n+1)\omega$ and $X\ncong {\mathbb{P}}^n$, then $\mathrm{vol}…