$L^{\mathrm{\infty }}$ estimates for Kähler-Ricci flow on Kähler-Einstein Fano manifolds: a new derivation

Assuming Perelman’s estimates, we give a new proof of uniform $L^{\mathrm{\infty }}$ estimate along normalized Kähler-Ricci flow on Fano manifolds with Kähler-Einstein metrics, using Chen-Cheng’s auxiliary Monge-Ampère equation and the Alexandrov-Bakelman-Pucci maximum principle. This proof does not use pluripotential theory.