-stability on toric manifolds

Authors:
Bin Zhou and Xiaohua Zhu

Journal:
Proc. Amer. Math. Soc. **136** (2008), 3301-3307

MSC (2000):
Primary 53C25; Secondary 32J15, 53C55, 58E11

Published electronically:
April 29, 2008

MathSciNet review:
2407096

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Abstract | References | Similar Articles | Additional Information

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.

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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:
https://doi.org/10.1090/S0002-9939-08-09485-9

Keywords:
$K$-stability,
toric manifolds,
extremal metrics

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

Article copyright:
© Copyright 2008
American Mathematical Society