We give an analogue of triangle comparison for Kähler manifolds with a lower bound on the holomorphic bisectional curvature. We show that the condition passes to noncollapsed Gromov–Hausdorff limits. We discuss tangent cones and singular Kähler spaces.
"Comparison geometry of holomorphic bisectional curvature for Kähler manifolds and limit spaces." Duke Math. J. 170 (14) 3039 - 3071, 1 October 2021. https://doi.org/10.1215/00127094-2021-0058