The Parabolic Quaternionic Monge-Ampère Type Equation on HyperKähler Manifolds

Abstract

This paper proves the long-time existence and uniqueness of solutions to a parabolic quaternionic Monge-Ampère type equation on compact hyperKähler manifolds. Moreover, it is shown that after normalization, the solution converges smoothly to the unique solution of the Monge-Ampère equation for (n − 1)-quaternionic psh functions.

Keywords

Quaternionic Monge-Ampère type equation / Parabolic equation / HyperKähler manifold / 53C26 / 58J35 / 32W20

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