A volume stability theorem on toric manifolds with positive Ricci curvature

Wang, Feng

doi:10.1090/proc/12174

A volume stability theorem on toric manifolds with positive Ricci curvature
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Proc. Amer. Math. Soc. 143 (2015), 3613-3618 Request permission

Abstract:

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 Kähler metric $\omega$ with Ricci curvature no less than $1$ and its volume is close to the volume of $\mathbb {CP}^n$, $M$ is bi-holomorphic to $\mathbb {CP}^n$.

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