Solvability of the quaternionic Monge-Ampere equation on compact manifolds with a flat hyperKaehler metric

Details Solvability of the quaternionic Monge-Ampere equation on compact manifolds with a flat hyperKaehler metric Solvability of the quaternionic Monge-Ampere equation on compact manifolds with a flat hyperKaehler metric

2011-08-30

arxiv.org/abs/1108.5910v2

Mathematics

Complex Variables

38 page; references

Scientific paper

A quaternionic version of the Calabi problem was recently formulated by M. Verbitsky and the author. It conjectures a solvability of a quaternionic Monge-Ampere equation on a compact HKT manifold (HKT stays for HyperKaehler with Torsion). In this paper this problem is solved under an extra assumption that the manifold admits a flat hyperKaehler metric compactible with the underlying hypercomplex structure. The proof uses the continuity method and a priori estimates.

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