Integration of differential forms on manifolds with locally finite variations.
Intermediate inversion formulas in integral geometry.
Invariant variational problems on principal bundles and conservation laws
In this work, we consider variational problems defined by -invariant Lagrangians on the -jet prolongation of a principal bundle , where is the structure group of . These problems can be also considered as defined on the associated bundle of the -th order connections. The correspondence between the Euler-Lagrange equations for these variational problems and conservation laws is discussed.
Inverse problem of the classical calculus of variations
Isospectral deformations of the Lagrangian Grassmannians
We study the special Lagrangian Grassmannian , with , and its reduced space, the reduced Lagrangian Grassmannian . The latter is an irreducible symmetric space of rank and is the quotient of the Grassmannian under the action of a cyclic group of isometries of order . The main result of this paper asserts that the symmetric space possesses non-trivial infinitesimal isospectral deformations. Thus we obtain the first example of an irreducible symmetric space of arbitrary rank , which is...
Isotopie de formes fermées en dimension trois.
L-когомологии искривленных цилиндров.
-когомология искривленных произведений липшицевых римановых многообразий
La trilogie du moment
A toute deux-forme fermée, sur une variété connexe, on associe une famille d’extensions centrales du groupe de ses automorphismes par son tore des périodes. On discute ensuite quelques propriétés de cette construction.
Lefschetz theorems for the integral leaves of a holomorphic one-form
Lemme de Morse transverse pour des puissances de formes de volume
Levi forms, differential forms of type (0,1) and pseudoconvexity in Banach spaces
Liftings of 1-forms to the -velocities bundle
Lifts of 1-forms to the tangent bundle of higher order
Local structural stability of integrable 1-forms
In this work we consider a class of germs of singularities of integrable 1-forms in which are structurally stable in class ( if , if ), whose 1-jet is zero at the singularity. In this class the stability depends essentially on the fact that the perturbations allowed are integrable.
Local symplectic algebra of quasi-homogeneous curves
We study the local symplectic algebra of parameterized curves introduced by V. I. Arnold. We use the method of algebraic restrictions to classify symplectic singularities of quasi-homogeneous curves. We prove that the space of algebraic restrictions of closed 2-forms to the germ of a 𝕂-analytic curve is a finite-dimensional vector space. We also show that the action of local diffeomorphisms preserving the quasi-homogeneous curve on this vector space is determined by the infinitesimal action of...
Modular vector fields and Batalin-Vilkovisky algebras
We show that a modular class arises from the existence of two generating operators for a Batalin-Vilkovisky algebra. In particular, for every triangular Lie bialgebroid (A,P) such that its top exterior power is a trivial line bundle, there is a section of the vector bundle A whose -cohomology class is well-defined. We give simple proofs of its properties. The modular class of an orientable Poisson manifold is an example. We analyse the relationships between generating operators of the Gerstenhaber...
New estimates for elliptic equations and Hodge type systems
We establish new estimates for the Laplacian, the div-curl system, and more general Hodge systems in arbitrary dimension , with data in . We also present related results concerning differential forms with coefficients in the limiting Sobolev space .
New weighted Poincaré-type inequalities for differential forms.
Non-decomposable Nambu brackets
It is well-known that the Fundamental Identity (FI) implies that Nambu brackets are decomposable, i.e. given by a determinantal formula. We find a weaker alternative to the FI that allows for non-decomposable Nambu brackets, but still yields a Darboux-like Theorem via a Nambu-type generalization of Weinstein’s splitting principle for Poisson manifolds.