A note on the $K$-stability on toric manifolds
Differential Geometry
2007-06-05 v1 Algebraic Geometry
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 also we show that the modified -energy is proper in the space of -invariant K\"ahler metrics for the case of toric surfaces which admit the extremal metrics.
Keywords
Cite
@article{arxiv.0706.0505,
title = {A note on the $K$-stability on toric manifolds},
author = {Bin Zhou and Xiaohua Zhu},
journal= {arXiv preprint arXiv:0706.0505},
year = {2007}
}