Approximately holomorphic geometry and estimated transversality on 2-calibrated manifolds

The notion of 2-calibrated structure, generalizing contact structures, smooth taut foliations, etc., is defined. Approximately holomorphic geometry as introduced by S. Donaldson for symplectic manifolds is extended to 2-calibrated manifolds. An estimated transversality result that enables to study the geometry of such manifolds is presented. To cite this article: A. Ibort, D. Martínez Torres, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

On the degrees of branched coverings over links

Let M and M′ be 3-manifolds and L a link in M′. We prove that, under certain conditions, the degree of a branched covering $\text{π}\text{:M→(M′,L)}$ is determined by the topological types of M and (M′,L). To cite this article: A.M. Salgueiro, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Une alternative sur l'entropie des groupesAn alternative about entropy of groups

We prove the following alternative: either there exists a finitely generated group with exponential growth whose entropy is zero, or there exists a universal constant M>0 such that the entropy of all non-elementary hyperbolic groups with cyclic centralizers and their non-elementary subgroups is at least M. To cite this article: V. Guirardel, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 743–746.     

Méthode d'éléments finis avec hybridisation frontière pour les problèmes de contact avec frottementFinite element method with Lagrange multipliers for contact problems with friction

In this Note, we propose a finite element method with Lagrange multipliers in order to approximate contact problems with friction. The discretized normal and tangential constraints at the candidate contact interface are expressed by using continuous piecewise linear Lagrange multipliers in the saddle-point formulation. An optimal error estimate is established and several numerical studies corresponding to this choice of the discretized normal and tangential constraints are achieved. To cite this article: L. Baillet, T. Sassi, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 917–922.     

Modélisation de structures électromagnétiques périodiques – matériaux bianisotropes avec mémoire

In this Note we propose a rigorous justification of the limit constitutive law of a periodic bi-anisotropic electromagnetic structure with memory. This study is based on the periodic unfolding method, introduced by D. Cioranescu, A. Damlamian and G. Griso, and is applied on the time domain and on the frequency domain. To cite this article: A. Bossavit et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

The loop product for 3-manifolds

Let M be a connected, closed, oriented and smooth manifold of dimension d. Let LM be the space of loops in M. Chas and Sullivan introduced the loop product, an associative product of degree ?d on the homology of LM. In this Note we aim at identifying 3-manifolds with “non-trivial” loop products. To cite this article: H. Abbaspour, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Existence of a solution to a dynamic unilateral contact problem for a cracked viscoelastic body

In this paper we study a dynamic unilateral contact problem with friction for a cracked viscoelastic body. The viscoelastic model is characterized by Kelvin–Voigt's law and a nonlocal friction law is investigated here. The existence of a solution to the problem is obtained by using a penalty method. Several estimates are obtained on the solution to the penalized problem, which enable us to pass to the limit by using compactness results. To cite this article: M. Cocou, G. Scarella, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Sur l'analyticité des applications CR lisses à valeurs dans un ensemble algébrique réelOn the analyticity of smooth CR maps into a real algebraic set

Let f:M→M′ be a $\text{C}{}^{\mathrm{\infty }}$-smooth CR mapping between a generic real analytic submanifold $\text{M?}\text{C}{}^{\mathrm{n}}$ and a real algebraic subset $\text{M′?}\text{C}{}^{\mathrm{n\prime }}$. We prove that if M is minimal at a point p and if M′ does not contain complex curves, then f is real-analytic at p. To cite this article: B. Coupet et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 953–956.     

Sur les variétés sous-riemanniennes de contact isotropes

In this Note, we show that contrary to the dimension 3 case, isotropic contact sub-Riemannian manifolds of dimension greater than 3 do not exist. To cite this article: A.-R. Mansouri, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Hypersurfaces compactes d'un fibré vectoriel riemannien à courbure moyenne prescriteCompact hypersurfaces of a Riemannian vector bundle with prescribed mean curvature

Let M be a compact Riemannian manifold, E a Riemannian vector bundle on M and Σ the sphere subbundle of E. We look for embeddings of Σ into E admitting prescribed mean curvatures of various types. To cite this article: P. Cherrier, A. Hanani, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 525–528.     

Polyconvexity equals rank-one convexity for connected isotropic sets in M2×2

We give a short, self-contained argument showing that, for compact connected sets in $\text{M}{}^{\mathrm{2\times 2}}$ which are invariant under the left and right action of SO(2), polyconvexity is equivalent to rank-one convexity (and even to lamination convexity). As a corollary, the same holds for O(2)-invariant compact sets. These results were first proved by Cardaliaguet and Tahraoui. We also give an example showing that the assumption of connectedness is necessary in the SO(2) case. To cite this article: S. Conti et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

A level-set formulation of immersed boundary methods for fluid–structure interaction problems

We propose a level set formulation of the immersed boundary method for fluid–structure problems in two and three dimensions. We prove that the resulting model verifies an energy estimate. To cite this article: G.-H. Cottet, E. Maitre, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Lefschetz pencil structures for 2-calibrated manifolds

We prove that for closed 2-calibrated manifolds there always exist Lefschetz pencil structures. This generalizes similar results for symplectic and contact manifolds. To cite this article: A. Ibort, D. Marti´nez Torres, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Invariant scale matrix hypothesis tests under elliptical symmetry

The usual assumption in multivariate hypothesis testing is that the sample consists of n independent, identically distributed Gaussian m-vectors. In this paper this assumption is weakened by considering a class of distributions for which the vector observations are not necessarily either Gaussian or independent. This class contains the elliptically symmetric laws with densities of the form f(X(n × m)) = ψ[tr(X ? M)′ (X ? M)Σ^?1]. For testing the equality of k scale matrices and for the sphericity hypothesis it is shown, by using the structure of the underlying distribution rather than any specific form of the density, that the usual invariant normal-theory tests are exactly robust, for both the null and non-null cases, under this wider class.     

La fonction maximale de Hardy–Littlewood sur une classe d'espaces métriques mesurables

In this Note, we study the behavior of the Hardy–Littlewood maximal function M on cusp manifolds in terms of the growth of the volume of the base space. In particular, we prove that for all 1<p₀<+∞ fixed, there exists such a manifold on which M is bounded on L^p for p>p₀ but not for 1?p<p₀. To cite this article: H.-Q. Li, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Approximation par la méthode des éléments finis de la formulation en domaine régulier de problèmes de fissures

The discretization by various mixed finite element methods of a new variational formulation of crack problems is considered. The new formulation, called the smooth domain method, is derived for crack problems in the case of a simplified model of an elastic membrane. Inequality type boundary conditions are prescribed at the crack faces. The resulting model takes the form of an unilateral contact problem on the crack. The mathematical analysis for the method leads to optimal convergence rates, as given in this Note. To cite this article: Z. Belhachmi et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

On the Compactness of the Hypercomplex Commutator in Hölder Continuous Functions Spaces

This paper is devoted to the compactness of the hypercomplex commutator S _γ M _a ? M _a S _γ, where S _γ is the Cauchy singular integral operator (in the Douglis sense), a is a Hölder continuous hypercomplex function and M _a is the multiplication operator given by M _a f = a f. We extend a known compactness sufficient condition for the commutator of the Cauchy singular integral operator to the frame of the hypercomplex analysis, where γ is merely required to be an arbitrary regular closed Jordan curve.     

La variété des classes analytiques d'équations aux q-différences dans une classe formelle

We describe the structure of affine algebraic variety of the set of analytical classes of q-difference equations within a given formal class. To cite this article: J.-P. Ramis et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Comportement asymptotique d'une grue

We study the asymptotic behaviour of a structure depending of two small parameters. The ratio of these two parameters plays a part in the limit problems. To cite this article: G. Griso, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Modules de Hodge sur les variétés de Shimura,et leur dégénérescence dans la compactification de Baily–Borel

We study the degeneration of variations of Hodge structure on Shimura varieties, which are given by algebraic representations. Our main result expresses this degeneration in terms of Hochschild, and abstract group cohomology. It is the Hodge theoretic analogue of Pink's theorem on degeneration of ?-adic sheaves [Math. Ann. 292 (1992) 197–240]. To cite this article: J.I. Burgos, J. Wildeshaus, C. R. Acad. Sci. Paris, Ser. I 336 (2003).