Seminar talk, 11 March 2009: Difference between revisions
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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. | 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. | ||
[[Category: Seminar|Seminar talk | [[Category: Seminar|Seminar talk 7990-96-88]] | ||
[[Category: Seminar abstracts|Seminar talk | [[Category: Seminar abstracts|Seminar talk 7990-96-88]] | ||
Latest revision as of 22:09, 17 September 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.