  In this short note we prove that a Kahler manifold with lower Ricci curvature
bound and almost maximal volume is Gromov-Hausdorff close to the projective
space with the Fubini-Study metric. This is done by combining the recent
results of Kewei Zhang and Yuchen Liu on holomorphic rigidity of such Kahler
manifolds with the structure theorem of Tian-Wang for almost Einstein
manifolds. This can be regarded as the complex analog of the result on Colding
on the shape of Riemannian manifolds with almost maximal volume
