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arXiv · 2305.09421

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

Wangjian Jian·Yalong Shi
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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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Wangjian Jian, Yalong Shi. 2023-05-16. $L^\infty$ estimates for K\"ahler-Ricci flow on K\"ahler-Einstein Fano manifolds: a new derivation. https://arxiv.org/abs/2305.09421

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