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arXiv · 0706.0505

A note on the $K$-stability on toric manifolds

Bin Zhou·Xiaohua Zhu
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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 also we show that the modified $K$-energy is proper in the space of $G_0$-invariant Kähler metrics for the case of toric surfaces which admit the extremal metrics.

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Bin Zhou, Xiaohua Zhu. 2007-06-04. A note on the $K$-stability on toric manifolds. https://arxiv.org/abs/0706.0505

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