 
Summary: communications in
analysis and geometry
Volume 15, Number 4, 669693, 2007
On the variational stability of
KšahlerEinstein metrics
Xianzhe Dai, Xiaodong Wang and Guofang Wei
Using spinc
structure we prove that KšahlerEinstein 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 defor
mations of the complex structure are integrable, then the Kšahler
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 KšahlerEinstein
metric.
1. Introduction
Stability issue comes up naturally in variational problems. One of the most
important geometric variational problems is that of the total scalar curvature
functional. Following [1, p. 132], we call an Einstein metric stable if the
