On a lower bound for the energy functional on a family of Hamiltonian minimal Lagrangian tori in $\mathbb{C}P^2$

Abstract

We study the energy functional on the set of Lagrangian tori in $\mathbb{C}P^2$ . We prove that the value of the energy functional on a certain family of Hamiltonian minimal Lagrangian tori in $\mathbb{C}P^2$ is strictly larger than energy of the Clifford torus.