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

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

2007-06-04

arxiv.org/abs/0706.0505v1

Mathematics

Differential Geometry

8 pages

Scientific paper

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 K\"ahler
metrics for the case of toric surfaces which admit the extremal metrics.

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