Geometric Convergence of the Kähler-Ricci Flow on Complex Surfaces of General Type

We show that on smooth minimal surfaces of general type, the Kähler-Ricci flow starting at any initial Kähler metric converges in the Gromov-Hausdorff sense to a Kähler-Einstein orbifold surface. In particular, the diameter of the evolving metrics is uniformly bounded for all time, and the Kähler-Ricci flow contracts all the holomorphic spheres with $(-2)$ self-intersection number to isolated orbifold points. Our estimates do not require a priori the existence of an orbifold Kähler-Einstein metric on the canonical model.