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 Kahler 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 (he case where the polarization class admits ail extremal Kahler metric, even when H is not semisimple.