$L^\infty$ estimates for K\"ahler-Ricci flow on K\"ahler-Einstein Fano manifolds: a new derivation

Assuming Perelman's estimates, we give a new proof of uniform $L^\infty$ estimate along normalized K\"ahler-Ricci flow on Fano manifolds with K\"ahler-Einstein metrics, using Chen-Cheng's auxiliary Monge-Amp\`ere equation and the Alexandrov-Bakelman-Pucci maximum principle. This proof does not use pluripotential theory.