Abstract We introduce a parabolic analogue of the elliptic split-type Monge-Ampère equation developed by Fang and the author, extending Streets’ twisted Monge-Ampère equation. The resulting equation is fully nonlinear and non-concave. We prove long-time existence for equations whose exponents are not too far apart and give conditions for convergence to the twisted Monge-Ampère when the exponents approach each other. Applications include long-time convergence on Kähler backgrounds and reduction to the twisted Monge-Ampère equation under curvature assumptions.
Joshua Jordan (Sat,) studied this question.