A Chern-Calabi flow on Hermitian manifolds (Q2117475)

The author studies an analogue of the Calabi flow in the non-Kähler setting for compact Hermitian manifolds with vanishing first Bott-Chern class. She gives a priori estimates for the evolving metric along the flow under a uniform bound of the Chern scalar curvature. If the Chern scalar curvature remains uniformly bounded for all time, she shows that the flow converges smoothly to the unique Chern-Ricci-flat metric in the \(\partial \overline{\partial}\)-class of the initial metric.