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

Dmitri V. Alekseevsky; Ricardo Alonso-Blanco; Gianni Manno; Fabrizio Pugliese

Displaying similar documents to “Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions”

Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks

Masafumi Yoshino, Todor Gramchev (2008)

Annales de l’institut Fourier

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We study the simultaneous linearizability of $d$ –actions (and the corresponding $d$ -dimensional Lie algebras) defined by commuting singular vector fields in $ℂ^{n}$ fixing the origin with nontrivial Jordan blocks in the linear parts. We prove the analytic convergence of the formal linearizing transformations under a certain invariant geometric condition for the spectrum of $d$ vector fields generating a Lie algebra. If the condition fails and if we consider the situation where small denominators...

The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables

Miroslav Zelený (2008)

Annales de l’institut Fourier

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We construct a differentiable function $f : R^{n} \to R$ ( $n \geq 2$ ) such that the set ${(\nabla f)}^{- 1} (B (0, 1))$ is a nonempty set of Hausdorff dimension $1$ . This answers a question posed by Z. Buczolich.

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let $A, B$ denote generic binary forms, and let $𝔲_{r} = {(A, B)}_{r}$ denote their $r$ -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the ${𝔲_{r}}$ . As a consequence, we show that each of the higher transvectants ${𝔲_{r} : r \geq 2}$ is redundant in the sense that it can be completely recovered from $𝔲_{0}$ and $𝔲_{1}$ . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of $S L_{2}$ -representations,...

OsckM admitting f-structure

Jovanka Nikić, Irena Čomić (2005)

Kragujevac Journal of Mathematics

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On the Fefferman-Phong inequality

Abdesslam Boulkhemair (2008)

Annales de l’institut Fourier

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We show that the number of derivatives of a non negative 2-order symbol needed to establish the classical Fefferman-Phong inequality is bounded by $\frac{n}{2} + 4 + ϵ$ improving thus the bound $2 n + 4 + ϵ$ obtained recently by N. Lerner and Y. Morimoto. In the case of symbols of type $S_{0, 0}^{0}$ , we show that this number is bounded by $n + 4 + ϵ$ ; more precisely, for a non negative symbol $a$ , the Fefferman-Phong inequality holds if $\partial_{x}^{α} \partial_{ξ}^{β} a (x, ξ)$ are bounded for, roughly, $4 \leq | α | + | β | \leq n + 4 + ϵ$ . To obtain such results and others, we first prove an abstract result which...