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.
Tue, 21/11/2017 - 12:00 to 13:30
Room 70A, Ross Building, Jerusalem, Israel