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 -stability on toric manifolds
Author(s):
Bin
Zhou;
Xiaohua
Zhu
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3301-3307.
MSC (2000):
Primary 53C25;
Secondary 32J15, 53C55, 58E11
Posted:
April 29, 2008
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Abstract:
In this note, we prove that on polarized toric manifolds the relative  -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  -energy is proper in the space of  -invariant Kähler potentials in the case of toric surfaces which admit the extremal metrics.
References:
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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.
- [ZZ2]
- Zhou, B., and Zhu, X.H., Minimizing weak solutions for calabi's extremal metrics on toric manifolds, Calculus in Variations and PDE, 32 (2008), 191-217.
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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
DOI:
10.1090/S0002-9939-08-09485-9
PII:
S 0002-9939(08)09485-9
Keywords:
$K$-stability,
toric manifolds,
extremal metrics
Received by editor(s):
July 17, 2007
Posted:
April 29, 2008
Additional Notes:
The second author was partially supported by NSF10425102 in China.
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2008,
American Mathematical Society
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