Almost all Lagrangian torus orbits in $\mathbb{C}{P}^n$ are not Hamiltonian volume minimizing

Abstract

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.

14 pages. arXiv admin note: text overlap with arXiv:1408.5576

References in corpus (1)

• Lagrangian product tori in tame symplectic manifolds