A gradient estimate for the Ricci-Kähler flow (Q5943915)

The article is devoted to a solution to the Ricci-Kähler flow: \(\partial g_{i,\bar j}/\partial t=-R_{i,\bar j}\), \(g(0)=g_0\). The following theorem is proved: If for a complete solution of the problem with curvature, potential, scalar curvature function and their gradients bounded by a constant depending on time, then the absolute value of the scalar curvature and the gradient squared of a modified potential function \(\tilde f\) are bounded by \(C/t\): \(R+\nabla {\tilde f}^2\leq C/t\).