The parabolic quaternionic Monge-Ampère type equation on hyperKähler manifolds

Abstract: We prove the long time existence and uniqueness of solution to a parabolic quaternionic Monge-Amp`{e}re type equation on a compact hyperK\"{a}hler manifold. We also show that after normalization, the solution converges smoothly to the unique solution of the Monge-Amp`{e}re equation for $(n-1)$-quaternionic psh functions.