METRICS OF CONSTANT CHERN SCALAR CURVATURE AND A CHERN-CALABI FLOW - XI SISI SHEN (COLUMBIA UNIVERSITY)

We discuss the existence problem of constant Chern scalar curvature metrics on a compact complex manifold. We prove a priori estimates for these metrics conditional on an upper bound on the entropy, extending a recent result by Chen-Cheng in the Kähler setting. In addition, we show how these estimates can be used to prove a convergence result for a Hermitian analogue of the Calabi flow on compact complex manifolds with vanishing first Bott-Chern class.

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