Diameter rigidity for Kähler manifolds with positive bisectional curvature (Q5925693)

Inspired by Li-Wang's diameter comparison theorem [\textit{G. Liu} and \textit{Y. Yuan}, Math. Z. 290, No. 3--4, 1055--1061 (2018; Zbl 1401.53061)] and Cheng's maximal diameter theorem, the authors show that a Kähler manifold with holomorphic bisectional curvature bounded from below by 1 and maximal diameter (\(\frac{\pi}{\sqrt{2}}\)) is isometric to complex projective space with the Fubini-Study metric. The strategy of the proof of the authors' theorem is to establish a monotonicity formula for a function arising from Lelong numbers of positive currents on \(\mathbb{CP}^n\). Note that the theorem does not hold for the curvature assumption (in the theorem) which was relaxed to a positive Ricci lower bound in the Kähler case.