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

2011/08/30 by Semyon Alesker, Alesker, Semyon · 1 citation
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.1108.5910

Abstract

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

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• A remark on the second order estimates for the quaternionic Calabi-Yau problem on hyperkähler manifolds

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