On the $2$-Systole of Stretched Enough Positive Scalar Curvature Metrics on $\mathbb{S}^2\times\mathbb{S}^2$

We use recent developments by Gromov and Zhu to derive an upper bound for the $2$-systole of the homology class of $\mathbb{S}^2\times\{\ast\}$ in a $\mathbb{S}^2\times\mathbb{S}^2$ with a positive scalar curvature metric such that the set of surfaces homologous to $\mathbb{S}^2\times\{\ast\}$ is wide enough in some sense.