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

TL;DR

This paper investigates the energy functional on Lagrangian tori in complex projective space, demonstrating that a specific family of Hamiltonian minimal Lagrangian tori has higher energy than the Clifford torus.

Contribution

It establishes a lower bound for the energy functional on a family of Hamiltonian minimal Lagrangian tori in , showing they exceed the energy of the Clifford torus.

Findings

Energy functional value exceeds that of Clifford torus

Identifies a lower bound for Hamiltonian minimal Lagrangian tori

Provides insight into the geometric properties of these tori

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.