Seminar talk, 11 March 2009

Speaker: Dmitry Tunitsky

Title: On the linearization of Monge-Ampère equations

Abstract:

The talk is devoted to the differential-geometric structures associated to the systems of Monge-Ampère equations on manifolds and their applications to the linearization of these equations. The systems of Monge-Ampère equations that locally equivalent to triangle and semitriangle systems, to systems linear in derivatives (semilinear) with constant coefficients, and to system in total differentials are considered. Effectively checkable conditions that a given Monge-Ampère system belongs to one of the above types are proved. As consequences, local conditions that a Monge-Ampère system reduces to one equation of second or first order are obtained.