Displaying similar documents to “Monge-Ampère equationsviewed from contact geometry”

Classification of Monge-Ampère equations with two variables

Boris Kruglikov (1999)

Banach Center Publications

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This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegenerate type. As an application we formulate a new method of finding symmetries. This together with previous author's results allows to state the solution of the classical S. Lie equivalence problem for the Monge-Ampère equations. ...

Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions

Dmitri V. Alekseevsky, Ricardo Alonso-Blanco, Gianni Manno, Fabrizio Pugliese (2012)

Annales de l’institut Fourier

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We study the geometry of multidimensional scalar 2 n d order PDEs (i.e. PDEs with n independent variables), viewed as hypersurfaces in the Lagrangian Grassmann bundle M ( 1 ) over a ( 2 n + 1 ) -dimensional contact manifold ( M , 𝒞 ) . We develop the theory of characteristics of in terms of contact geometry and of the geometry of Lagrangian Grassmannian and study their relationship with intermediate integrals of . After specializing such results to general...

Convergence in Capacity

Yang Xing (2008)

Annales de l’institut Fourier

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We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures which is essentially equivalent to convergence in the capacity C n of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity C n - 1 of functions in some case. As applications we give certain stability...

Contact geometry of curves.

Vassiliou, Peter J. (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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