Real and complex Monge-Ampere equations play a central role in several

branches of geometry and analysis. We introduce a quaternionic version

of a Monge-Ampere equation which is an analogue of the famous Calabi

problem in the complex case. It is a non-linear elliptic equation of second

order on so called HyperKahler with Torsion (HKT) manifolds (the latter

manifolds were introduced by physicists in 1990's). While in full generality

it is still unsolved, we will describe its solution in a special case and some

partial results towards its proof in the general case. Part of the results are

joint with M. Verbitsky and E. Shelukhin.

branches of geometry and analysis. We introduce a quaternionic version

of a Monge-Ampere equation which is an analogue of the famous Calabi

problem in the complex case. It is a non-linear elliptic equation of second

order on so called HyperKahler with Torsion (HKT) manifolds (the latter

manifolds were introduced by physicists in 1990's). While in full generality

it is still unsolved, we will describe its solution in a special case and some

partial results towards its proof in the general case. Part of the results are

joint with M. Verbitsky and E. Shelukhin.

## Date:

Tue, 21/11/2017 - 12:00 to 13:30

## Location:

Room 70A, Ross Building, Jerusalem, Israel