Relative $K$-stability and modified $K$-energy on toric manifolds
Differential Geometry
2007-05-23 v1
Abstract
In this paper, we discuss the relative -stability and the modified -energy associated to the Calabi's extremal metric on toric manifolds. We give a sufficient condition in the sense of convex polytopes associated to toric manifolds for both the relative -stability and the properness of modified -energy. In particular, our results hold for toric Fano manifolds with vanishing Futaki-invariant. We also verify our results on the toric Fano surfaces.
Keywords
Cite
@article{arxiv.math/0603237,
title = {Relative $K$-stability and modified $K$-energy on toric manifolds},
author = {Bin Zhou and Xiaohua Zhu},
journal= {arXiv preprint arXiv:math/0603237},
year = {2007}
}