The parabolic quaternionic Calabi–Yau equation on hyperkähler manifolds

Abstract

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