On the Stability of K\"ahler-Einstein Metrics
Differential Geometry
2007-05-23 v1
Abstract
Using spin structure we prove that K\"ahler-Einstein metrics with nonpositive scalar curvature are stable (in the direction of changes in conformal structures) as the critical points of the total scalar curvature functional. Moreover if all infinitesimal complex deformation of the complex structure are integrable, then the K\"ahler-Einstein metric is a local maximal of the Yamabe invariant, and its volume is a local minimum among all metrics with scalar curvature bigger or equal to the scalar curvature of the K\"ahler-Einstein metric.
Cite
@article{arxiv.math/0504527,
title = {On the Stability of K\"ahler-Einstein Metrics},
author = {Xianzhe Dai and Xiaodong Wang and Guofang Wei},
journal= {arXiv preprint arXiv:math/0504527},
year = {2007}
}