Interior derivative estimates for the Kähler–Ricci flow

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We give a maximum principle proof of interior derivative estimates for the K\"ahler-Ricci flow, assuming local uniform bounds on the metric.

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Infinite time singularities of the Kähler-Ricci flow (2014, background): “3] and is an adaptation (and in fact a special case) of a similar result from [19] for the Kähler–Ricci flow.”
Kähler currents and null loci (2013, methodology): “The local higher order estimates of Sherman and Weinkove [43], then give us C∞ estimates for ω on U ′ × [0, T ) for a slightly smaller open neighborhood U ′ of x , and from here we conclude as in the proof of Theorem 4.”