  All principal orbits of the standard Hamiltonian $T^n$-action on the complex
projective space ${\mathbb C}P^n$ are Lagrangian tori.In this article, we prove
that most of them are not volume minimizing under Hamiltonian isotopies of
${\mathbb C}P^n$ if the complex dimension $n$ is greater than two, although
they are Hamiltonian minimal and Hamiltonian stable.
