Almost all standard Lagrangian tori in Cⁿ are not Hamiltonian volume minimizing

الأصل · EN

In 1993, Y.-G. Oh proposed a problem whether standard Lagrangian tori in Cⁿ are volume minimizing under Hamiltonian isotopies of Cⁿ. In this article, we prove that most of them do not have such property if the dimension n is greater than two. We also discuss the existence of Hamiltonian non-volume minimizing Lagrangian torus orbits of compact toric Kahler manifolds.