Smooth approximation of conic Kähler metric with lower Ricci curvature bound (Q312768)

Recently, very important progress has been made on Kähler-Einstein metrics on Fano manifolds using an extension of the Cheeger-Colding-Tian theory. Now, a more general problem is to understand the structures of Kähler manifolds with lower Ricci curvature bound and the present paper is devoted to this interesting question. We recall that a smooth Kähler metric \(\omega _0\) has a lower Ricci curvature bound \(\mu \) if there exists a non-negative \((1, 1)\)-form \(\Omega _0\) such that \(\mathrm{Ric}\,\omega _0=\mu \omega _0+\Omega _0\).