Alesker, S. and Verbitski, M. (2010) Quaternionic Monge-Ampère equation and Calabi problem for HKT-manifolds. Israel Journal of Mathematics, 176(1), pp. 109-138. (doi: 10.1007/s11856-010-0022-0)
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Publisher's URL: http://dx.doi.org/10.1007/s11856-010-0022-0
Abstract
A quaternionic version of the Calabi problem on the Monge–Ampere equation is introduced, namely a quaternionic Monge–Ampere 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, as 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.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Verbitski, Dr Mikhail |
| Authors: | Alesker, S., and Verbitski, M. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Israel Journal of Mathematics |
| ISSN: | 0021-2172 |
| ISSN (Online): | 1565-8511 |
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