The parabolic quaternionic Calabi-Yau equation on hyperkähler manifolds (2303.02689v3)

Abstract: We show that the parabolic quaternionic Monge-Amp`ere equation on a compact hyperk\"ahler manifold has always a long-time solution which once normalized converges smoothly to a solution of the quaternionic Monge-Amp`ere equation. This is the same setting in which Dinew and Sroka prove the conjecture of Alesker and Verbitsky. We also introduce an analogue of the Chern-Ricci flow in hyperhermitian manifolds.