  We consider canonical metrics on Fano manifolds. First we introduce a
norm-type functional on Fano manifolds, which has Kahler-Einstein or
Kahler-Ricci soliton as its critical point and the Kahler-Ricci flow can be
viewed as its (reduced) gradient flow. We then obtain a natural lower bound of
this functional. As an application, we prove that Kahler-Ricci soliton, if
exists, maximizes Perelman's $\mu$-functional without extra assumptions. Second
we consider a conjecture proposed by S.K. Donaldson in terms of $\cK$-energy.
Our simple observation is that $\cF$-functional, as $\cK$-energy, also
integrates Futaki invariant. We then restate geodesic stability conjecture on
Fano manifolds in terms of $\cF$-functional. Similar pictures can also be
extended to Kahler-Ricci soliton and modified $\cF$-functional.
