Eigenvalues estimate for the Neumann problem on bounded domains

In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a bounded domain (with smooth boundary) in a given complete (not compact a priori) Riemannian manifold with Ricci bounded below . For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general metric way, interesting for itself. As application, we get upper bounds for the Neumann spectrum which is clearly in agreement with the Weyl law and which is analogous to Buser's upper bounds of the spectrum of a closed Riemannian manifold with lower bound on the Ricci curvature.Comment: 9 pages, submitted december 200

A mass for asymptotically complex hyperbolic manifolds

We prove a positive mass theorem for complete K\"ahler manifolds that are asymptotic to the complex hyperbolic space

Killing Initial Data on Totally Umbilical & Compact Hypersurfaces

In this note, we give a geometric characterization of the compact and totally umbilical hypersurfaces that carry a non trivial locally static Killing Initial Data (KID). More precisely, such compact hypersurfaces have constant mean curvature and are isometric to one of the following manifolds: (i) Sn the standard sphere, (ii) a finite quotient of a warped product of a circle with a compact Einstein manifold of positive scalar curvature. In particular, these hypersurfaces have harmonic curvature and strictly positive constant scalar curvature.Comment: 20 pages, submitted january 200

A Penrose-like inequality for maximal asymptotically flat spin initial data sets

We prove a Penrose-like inequality for the mass of a large class of constant mean curvature (CMC) asymptotically flat n-dimensional spin manifolds which satisfy the dominant energy condition and have a future converging, or past converging compact and connected boundary of non-positive mean curvature and of positive Yamabe invariant. We prove that for every n≥ 3 the mass is bounded from below by an expression involving the norm of the linear momentum, the volume of the boundary, dimensionless geometric constants and some normalized Sobolev rati

Optimal eigenvalue estimate for the Dirac-Witten operator on bounded domains with smooth boundary

Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and chiral conditions). This result is a generalisation of Friedrich's inequality for the usual Dirac operator. The limiting cases are also investigated.Comment: 2007, 18 pages, submitted 02 June 200

Eigenvalues Estimate for the Neumann Problem ofaBounded Domain

In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a domain Ω in a given complete (not compact a priori) Riemannian manifold (M,g). For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general metric way, interesting for itself. As applications, we prove that if the Ricci curvature of (M,g) is bounded below Ric  g ≥−(n−1)a 2, a≥0, then there exist constants A n >0,B n >0 only depending on the dimension, such that $$\lambda _{k}(\Omega)\le A_{n}a^{2}+B_{n}\left(\frac{k}{V}\right)^{2/n},$$ where λ k (Ω) (k∈ℕ*) denotes the k-th eigenvalue of the Neumann problem on any bounded domain Ω⊂M of volume V=Vol (Ω,g). Furthermore, this upper bound is clearly in agreement with the Weyl law. As a corollary, we get also an estimate which is analogous to Buser's upper bounds of the spectrum of a compact Riemannian manifold with lower bound on the Ricci curvatur

Rigid upper bounds for the angular momentum and centre of mass

We prove upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets satisfying the dominant energy condition. We work in all space-dimensions larger than or equal to three, and allow a large class of asymptotic backgrounds, with spherical and non-spherical conformal infinities; in the latter case, a spin-structure compatibility condition is imposed. We give a large class of non-trivial examples saturating the inequality. We analyse exhaustively the borderline case in space-time dimension four: for spherical cross-sections of Scri, equality together with completeness occurs only in anti-de Sitter space-time. On the other hand, in the toroidal case, regular non-trivial initial data sets saturating the bound exist

Review of Electrochemically Triggered Macromolecular Film Buildup Processes and Their Biomedical Applications

International audienceMacromolecular coatings play an important role in many technological areas, ranging from the car industry to biosensors. Among the different coating technologies, electrochemically triggered processes are extremely powerful because they allow in particular spatial confinement of the film buildup up to the micrometer scale on microelectrodes. Here, we review the latest advances in the field of electrochemically triggered macromolecular film buildup processes performed in aqueous solutions. All these processes will be discussed and related to their several applications such as corrosion prevention, biosensors, antimicrobial coatings, drug-release, barrier properties and cell encapsulation. Special emphasis will be put on applications in the rapidly growing field of biosensors. Using polymers or proteins, the electrochemical buildup of the films can result from a local change of macromolecules solubility, self-assembly of polyelectrolytes through electrostatic/ionic interactions or covalent cross-linking between different macromolecules. The assembly process can be in one step or performed step-by-step based on an electrical trigger affecting directly the interacting macromolecules or generating ionic species

“His Heart Beat With The Avidity of a Young Lover”: The Unattainable Object of Desire in Joyce Carol Oates’s “The Skull: A Love Story”

La nouvelle de Joyce Carol Oates, « The Skull: A Love Story », possède indéniablement des accents poesques. Cependant, plus qu’un simple récit gothique ou policier, cette nouvelle est avant tout le portrait psychologique convaincant de son protagoniste. Suivant la théorie de Barthes selon laquelle désir et récit sont intimement liés, cet article vise à montrer que la nouvelle de Oates peut aussi être lue comme une métaphore de l’acte d’écriture. Prenant comme point de départ les fragments d’un crâne brisé, Cassidy se base essentiellement sur des suppositions pour recréer une version idéalisée de la défunte. Le récit met l’accent sur le manque, et le désir ici naît de l'absence. L’empressement du protagoniste à combler les failles de l’enquête fait écho à son désir de combler ses propres vides affectifs. En tentant vainement de s’approprier l’objet de son désir, Cassidy semble plutôt vouloir flatter ses penchants narcissiques et son désir masculin de « révérence ». En outre, le parallèle que dresse le récit entre la victime et la fille illégitime de Cassidy – sa « présence absente » pour emprunter le concept de Derrida – soulève la question de l’inceste œdipien déjà contenue dans le paradigme de Pygmalion tombant amoureux de sa propre création, renforçant ainsi la métaphore de l’écriture puisque, selon Barthes, « tout récit ne se ramène-t-il pas à l’Œdipe ?