Quaternionic Monge-Ampère equation and Calabi problem for HKT-manifolds
By Semyon Alesker, Misha Verbitsky. 2008
81 citations recorded by the source corpus.
A quaternionic version of the Calabi problem on the Monge-Ampère equation is introduced, namely a quaternionic Monge-Ampère equation on a compact hypercomplex manifold with an HKT-metric. The equation is non-linear elliptic of second order. For a hypercomplex manifold with holonomy in SL(n,ℍ), uniqueness (up to a constant) of a solution is proven, aas well as the zero order a priori estimate. The existence of a solution is conjectured, similar to the Calabi-Yau theorem. We reformulate this quaternionic equation as a special case of the complex Hessian equation, making sense on any complex manifold.
Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/7145a557ce9d2fb6ae3bd62281e27b1bcb6f8226
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In Applied Mathematics
In Geometry and Topology
In Nuclear and High Energy Physics
Citations in the corpus
- Degenerate complex Hessian equations on compact K\"ahler manifolds (2014, background): “In [1] equations of complex Hessian type appear in the study of quaternionic geometry.”