preprint
Inserted: 24 mar 2025
Last Updated: 24 mar 2025
Year: 2025
Abstract:
In this survey, we consider various analytic problems related to the geometry of the Chern connection on Hermitian manifolds, such as the existence of metrics with constant Chern-scalar curvature, generalizations of the K\"ahler-Einstein condition to the non-K\"ahler setting, and the convergence of the Chern-Ricci flow on compact complex surfaces.