The parabolic quaternionic Calabi–Yau equation on hyperkähler manifolds

We show that the parabolic quaternionic Monge–Ampère equation on a compact hyperkähler manifold has always a long-time solution which, once normalized, converges smoothly to a solution of the quaternionic Monge–Ampère equation. This is the same setting in which Dinew and Sroka (2023) prove the conjecture of Alesker and Verbitsky (2010). We also introduce an analogue of the Chern–Ricci flow in hyperhermitian manifolds.