Quaternionic Monge-Ampere equation and Calabi problem for HKT-manifolds

Details Quaternionic Monge-Ampere equation and Calabi problem for HKT-manifolds Quaternionic Monge-Ampere equation and Calabi problem for HKT-manifolds

2008-02-28

arxiv.org/abs/0802.4202v3

Israel J. Math. 176 (2010), 109-138

Mathematics

Complex Variables

32 pages, minor corrections

Scientific paper

A quaternionic version of the Calabi problem on Monge-Ampere equation is introduced. It is 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 solution is conjectured, similar to Calabi-Yau theorem. We reformulate this quaternionic equation as a special case of a complex Hessian equation, making sense on any complex manifold.

Affiliated with

Also associated with

No associations

Rating

Quaternionic Monge-Ampere equation and Calabi problem for HKT-manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quaternionic Monge-Ampere equation and Calabi problem for HKT-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quaternionic Monge-Ampere equation and Calabi problem for HKT-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-471839