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Let ( M,g(t)) be a K\"ahler Ricci flow with positive first Chern class. First, we prove a uniform isoperimetric inequality for all time. In the process, we also prove a Cheng-Yau type log gradient bound for positive harmonic functions on ( M,g(t)) without assuming the Ricci curvature is bounded from below.
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Tian et al. (2014) studied this question.
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