A C¹ bound on smooth curves of Hermitian metrics implies new regularity for Hermitian curvature flows.
Yau , On the Ricci curvature of a compact K\"ahler manifold and the complex Monge-Amp\`ere equation, I, Comm
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On the Calabi estimate of geometric flows of Hermitian metrics
A C¹ bound on smooth curves of Hermitian metrics implies new regularity for Hermitian curvature flows.