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The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 1080–1097 | Cite as

Convergence of the Calabi Flow on Toric Varieties and Related Kähler Manifolds

  • Hongnian HuangEmail author
Article

Abstract

Let X be a toric manifold with a Delzant polytope P. We show that if (X,P) is analytic uniform K-stable and the curvature is uniformly bounded along the Calabi flow, then the modified Calabi flow converges to an extremal metric exponentially fast. By assuming that the curvature is uniformly bounded along the Calabi flow, we prove a conjecture of Donaldson and a conjecture of Apostolov, Calderbank, Gauduchon, and Tønnesen-Friedman.

Keywords

Calabi flow Toric manifolds Extremal metrics K-stability 

Mathematics Subject Classification

53C44 53C55 53D20 

Notes

Acknowledgements

The author would like to thank Vestislav Apostolov and Gábor Székelyhidi for many stimulating discussions. He is also grateful to the consistent support of Professor Xiuxiong Chen, Pengfei Guan, and Paul Gauduchon. He would like to thank Si Li, Jeff Streets, and Valentino Tosatti for their interest in this work.

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Copyright information

© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  1. 1.CMLSÉcole PolytechniquePalaiseauFrance

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