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A volume stability theorem on toric manifolds with positive Ricci curvature


Author: Feng Wang
Journal: Proc. Amer. Math. Soc. 143 (2015), 3613-3618
MSC (2010): Primary 53C23; Secondary 53C55
DOI: https://doi.org/10.1090/proc/12174
Published electronically: April 22, 2015
MathSciNet review: 3348802
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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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Additional Information

Feng Wang
Affiliation: School of Mathematical Science, Beijing University, Beijing, People’s Republic of China 100871
Email: fengwang232@gmail.com

DOI: https://doi.org/10.1090/proc/12174
Keywords: Differential geometry
Received by editor(s): November 3, 2012
Received by editor(s) in revised form: February 19, 2013
Published electronically: April 22, 2015
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.