A volume stability theorem on toric manifolds with positive Ricci curvature

Wang Feng

A volume stability theorem on toric manifolds with positive Ricci curvature

Differential Geometry 2012-10-23 v1

Authors: Wang Feng

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 K\"ahler 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 $\mathbb{CP}^n$ .

Keywords

volume stability theorem toric manifolds positive Ricci curvature Kähler metric bi-holomorphic complex projective space

Cite

@article{arxiv.1210.5711,
  title  = {A volume stability theorem on toric manifolds with positive Ricci curvature},
  author = {Wang Feng},
  journal= {arXiv preprint arXiv:1210.5711},
  year   = {2012}
}

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