Resumen de Hermitian curvature flow

Jeffrey D. Streets, Gang Tian

• We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler�Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler�Einstein metrics, and are automatically Kähler�Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler�Einstein metrics with negative or zero first Chern class.