𝐾-stability on toric manifolds

Zhou, Bin; Zhu, Xiaohua

doi:10.1090/S0002-9939-08-09485-9

$K$-stability on toric manifolds
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by Bin Zhou and Xiaohua Zhu

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

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

Published electronically: April 29, 2008

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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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