Let $(M,J)$ be a compact complex manifold, and
let $E\subset H^{1,1}(M,\mathbb{R})$ be the set of all cohomology classes which can be represented by Kähler forms of extremal Kähler metrics.
Then $E$ is an open set.
References
[LS94] C. LeBrun and S. R. Simanca.
Extremal Kähler metrics and complex deformation theory. Geom. Funct. Anal., 4(3):298-336, 1994.
[LS05] Claude LeBrun and Santiago R. Simanca.
On the Kähler classes of extremal metrics. 26/05/2005.