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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$K$-stability on toric manifolds
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by Bin Zhou and Xiaohua Zhu PDF
Proc. Amer. Math. Soc. 136 (2008), 3301-3307 Request permission

Abstract:

In this note, we prove that on polarized toric manifolds the relative $K$-stability with respect to Donaldson’s toric degenerations is a necessary condition for the existence of Calabi’s extremal metrics, and we also show that the modified $K$-energy is proper in the space of $G_0$-invariant Kähler potentials in the case of toric surfaces which admit the extremal metrics.
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  • Zhou, B., and Zhu, X.H., Relative K-stability and modified K-energy on toric manifolds, to appear in Advances in Math.
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Additional Information
  • Bin Zhou
  • Affiliation: Department of Mathematics, Peking University, Beijing, 100871, People’s Republic of China
  • Xiaohua Zhu
  • Affiliation: Department of Mathematics, Peking University, Beijing, 100871, People’s Republic of China
  • Email: xhzhu@math.pku.edu.cn
  • Received by editor(s): July 17, 2007
  • Published electronically: April 29, 2008
  • Additional Notes: The second author was partially supported by NSF10425102 in China.
  • Communicated by: Jon G. Wolfson
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3301-3307
  • MSC (2000): Primary 53C25; Secondary 32J15, 53C55, 58E11
  • DOI: https://doi.org/10.1090/S0002-9939-08-09485-9
  • MathSciNet review: 2407096