Ideals of the Lie algebras of vector fields
Ideas of Hugo Steinhaus in contemporary mathematics
Il teorema del trasporto per un'interfaccia in moto attraverso una regione di controllo
Il teorema di Morse-Sard in spazi di Sobolev Problemi di trasporto ottimale e applicazioni
Images inverses des modules différentiels
Implicit function theorem for locally blow-analytic functions
In this paper we prove the implicit function theorem for locally blow-analytic functions, and as an interesting application of using blow-analytic homeomorphisms, we describe a very easy way to resolve singularities of analytic curves.
Implicit functions from locally convex spaces to Banach spaces
We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller -map f defined on an open subset of E×F and with values in F, for E an arbitrary Hausdorff locally convex space and F a Banach space. As an application, we prove that under a certain transversality condition the preimage of a submanifold is a submanifold for a map from a Fréchet manifold to a Banach manifold.
Implicit quasilinear differential systems: A geometrical approach.
Impossible Einstein-Weyl geometries
In the joint paper of the author with K. P. Tod [J. Reine Angew. Math. 491, 183-198 (1997; Zbl 0876.53029)] they showed all local solutions of the Einstein-Weyl equations in three dimensions, where the background metric is homogeneous with unimodular isometry group. In particular, they proved that there are no solutions with Nil or Sol as background metric. In this note, these two special cases are presented.
Improved estimates for the Ginzburg-Landau equation : the elliptic case
We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the -energy and the parameter . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.
Impulsive boundary value problems for -Laplacian’s via critical point theory
In this paper we investigate the existence of solutions to impulsive problems with a -Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order to get the existence...
In Ehresmann's footsteps: from group geometries to groupoid geometries
The geometric understanding of Cartan connections led Charles Ehresmann from the Erlangen program of (abstract) transformation groups to the enlarged program of Lie groupoid actions, via the basic concept of structural groupoid acting through the fibres of a (smooth) principal fibre bundle or of its associated bundles, and the basic examples stemming from the manifold of jets (fibred by its source or target projections). We show that the remarkable relation arising between the actions of the structural...
In memory of Wiesław Szlenk
In the heart of representable metric jets
Index and dynamics of quantized contact transformations
Quantized contact transformations are Toeplitz operators over a contact manifold of the form , where is a Szegö projector, where is a contact transformation and where is a pseudodifferential operator over . They provide a flexible alternative to the Kähler quantization of symplectic maps, and encompass many of the examples in the physics literature, e.g. quantized cat maps and kicked rotors. The index problem is to determine when the principal symbol is unitary, or equivalently to determine...
Index and stability of harmonic Gauss maps.
Index formulas for pseudodifferential operators with discontinuous symbols
Index invariants of orbit spaces.
Index of transversally elliptic D-modules
Index theory and elliptic boundary value problems. Remarks and open problems