We construct local and global solutions to the Kähler–Ricci flow from a noncollapsed Kähler manifold with curvature bounded from below. Combining with the mollification technique of McLeod–Simon–Topping, we show that the Gromov–Hausdorff limit of a sequence of complete noncompact noncollapsed Kähler manifolds with orthogonal bisectional curvature and Ricci curvature bounded from below is homeomorphic to a complex manifold. We also use it to study the complex structure of complete Kähler manifolds with nonnegative orthogonal bisectional curvature, nonnegative Ricci curvature and maximal volume growth.
"Kähler manifolds with almost nonnegative curvature." Geom. Topol. 25 (4) 1979 - 2015, 2021. https://doi.org/10.2140/gt.2021.25.1979