K-stability on toric manifolds

Zhou, Bin; Zhu, Xiaohua

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K-stability on toric manifolds

Date

2008-04-29

Authors

Zhou, Bin

Zhu, Xiaohua

Publisher

American Mathematical Society

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 G₀-invariant Kähler potentials in the case of toric surfaces which admit the extremal metrics.