In  the authors introduced a parabolic flow of pluriclosed metrics. Here we give improved regularity results for solutions to this equation. Furthermore, we exhibit this equation as the gradient flow of the lowest eigenvalue of a certain Schrödinger operator, and show the existence of an expanding entropy functional for this flow. Finally, we motivate a conjectural picture of the optimal regularity results for this flow, and discuss some of the consequences.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Geometric flow
- Hermitian geometry