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

Published 16 May 2023 in math.DG | (2305.09421v1)

Abstract: 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.

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