Spectral almost rigidity on Kähler manifolds with positive Ricci lower bound

In this work, a sharp Kähler spectral almost-rigidity theorem was established, resolving Conjecture 1.8 of Chu--Wang--Zhang. For compact Kähler manifolds satisfying $\Ric(ω)\geqω$, pinching the first $n^2+3$ nonzero complex eigenvalues to one forces the manifolds to be Gromov Hausdorff close to norm