The Calabi-Yau equation for Lagrangian fibrations

Description:  The Calabi-Yau equation on Almost-Kaehler manifolds is an elliptic equation arising from a natural generalization of the Calabi conjecture to the non-complex context. This equation was introduced by Donaldson who proved that its solutions are unique and Tosatti, Weinkove and Yau proved that it can be solved under some assumptions . In a recent paper  Tosatti and Weinkove studied the Calabi-Yau equation on the Kodaira-Thurston manifold showing that it can be solved if the initial data is T^2-invariant. The Kodaira-Thurston manifold is a T^2-bunldle over a torus equipped with an invariant Lagrangian almost-Kaehler structure. In this talk I'll explain as the Tosatti-Weinkove theorem can be extended to every T^2-bundle over a T^ reducing the problem to a classical Monge-Ampère equation on a flat torus. This result is part of a work in progress with A. Fino, S.M. Salamon and Y.Y. Li. Date:  2010-12-15 Start Time:   12:00 Speaker:  Luigi Vezzoni (Università di Torino, Italy) Institution:  -- Place:  Room 5.4 Research Groups: -Geometry See more:   <Main>