Hypercomplex manifolds are manifolds equipped with a triple of complex structures I, J, K satisfying quaternionic relations. There is a direct analogue of Kaehler metrics in hypercomplex geometry, called HKT metrics; locally, such metrics always have a potential. This allows one to write a version of Monge-Ampere equations for a hypercomplex manifold. The hypercomplex Monge-Ampere equations can be interpreted in terms of complex geometry, as certain (very simple) Hessian equations. A conjectural version of Calabi-Yau theorem is proposed; uniqueness of solutions of Monge-Ampere proved. This is a joint work with Semyon Alesker.

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