Eguchi–Hanson limit conjecture for Kähler–Einstein edge metrics on the second Hirzebruch surface

Let ${\mathbb F}_2$ be the second Hirzebruch surface, equipped with the family of Kähler–Einstein edge metrics $\omega_{\beta_1,\beta_2}$ described in the source, with $\beta_1\in(0,1)$ and $\beta_2$ determined by $\beta_1$. Eguchi–Hanson limit conjecture. As $\beta_1$ tends to $1$, an appropriate limit of $({\mathbb F}_2,\omega_{\beta_1,\beta_2})$ converges to the Eguchi–Hanson metric. This prediction concerns the large-angle degeneration of Kähler–Einstein edge metrics; the paper's abstract states that it resolves the prediction by describing the relevant Gromov–Hausdorff limits.