A proof of the Willmore-type conjecture in $\mathbb{C}{P}^2$

Peng Wang, Zhenxiao Xie, Chen Zhao

In 2002, Montiel and Urbano conjectured that the Clifford torus in $\mathbb{C}{P}^2$ minimizes the Willmore-type functional ${\mathcal{W}}^{-}={\int }_{T^2}(2+|H{|}^2)dA,$ either among all…