2006/03/09 by Bin Zhou, Zhou, Bin, Xiaohua Zhu +1
Mathematics · Environmental Science · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Toxic Organic Pollutants Impact
paper · pdf · doi:10.48550/arxiv.math/0603237
In this paper, we discuss the relative K-stability and the modified K-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 K-stability and the properness of modified K-energy. In particular, our results hold for toric Fano manifolds with vanishing Futaki-invariant. We also verify our results on the toric Fano surfaces.