An energy-theoretic approach to the Hitchin-Kobayashi correspondence for   manifolds, II
  Recently, Donaldson proved asymptotic stability for a polarized algebraic manifold $M$ with polarization class admitting a K\"ahler metric of constant scalar curvature, essentially when the linear algebraic part $H$ of $Aut^0(M)$ is semisimple. The purpose of this paper is to give a generalization of Donaldson's result to the case where the polarization class admits an extremal K\"ahler metric, even when $H$ is not semisimple. 
Toshiki Mabuchi