Hamiltonian stability of Lagrangian tori in toric Kahler manifolds

Let (M, J, omega) be a compact toric Kahler manifold of dim(C) M = n and L a regular orbit of the T-n-action on M. In the present paper, we investigate Hamiltonian stability of L, which was introduced by Y.-G. Oh (Invent. Math. 101, 501-519 (1990); Math. Z. 212, 175-192) (1993)). As a result, we prove any regular orbit is Hamiltonian stable when (M, omega) = (CPn, omega(FS)) and (M, omega) = (CPn1 x CPn2 ,a omega(FS) circle plus b omega(FS)), where omega(FS) is the Fubini-Study Kahler form and a and b are positive constants. Moreover, they are locally Hamiltonian volume minimizing Lagrangian submanifolds.