  We show that the Mabuchi energy of any polarized manifold (X,L) is (bounded
below) proper on the full space of Kahler metrics in the first Chern class of L
if and only if (X,L) is asymptotically (semi)stable. In particular it now
follows from work of Xiuxiong Chen and Jinguri Cheng that there exists a cscK
metric in the first Chern class of L if and only if (X,L) is asymptotically
stable, provided the reduced automorphism group of (X,L) is finite.
