Embedded, doubly periodic minimal surfaces.
Embedded minimal surfaces with an infinite number of ends.
Embedding and surrounding with positive mean curvature.
Embedding of open riemannian manifolds by harmonic functions
Let be a noncompact Riemannian manifold of dimension . Then there exists a proper embedding of into by harmonic functions on . It is easy to find harmonic functions which give an embedding. However, it is more difficult to achieve properness. The proof depends on the theorems of Lax-Malgrange and Aronszajn-Cordes in the theory of elliptic equations.
Embedding Riemannian Manifolds by Their Heat Kernel.
Embedding theorems and Kahlerity for 1-convex spaces.
Energy and Morse index of solutions of Yamabe type problems on thin annuli
We consider the Yamabe type family of problems , in , on , where is an annulus-shaped domain of , , which becomes thinner as . We show that for every solution , the energy as well as the Morse index tend to infinity as . This is proved through a fine blow up analysis of appropriate scalings of solutions whose limiting profiles are regular, as well as of singular solutions of some elliptic problem on , a half-space or an infinite strip. Our argument also involves a Liouville type theorem...
Energy concentration for the Landau–Lifshitz equation
Energy machineries on a manifold; application to the construction of new energy representations of Gauge groups.
The introduction of the concepts of energy machinery and energy structure on a manifold makes it possible a large class of energy representations of gauge groups including, as a very particular case, the ones known up to now. By using an adaptation of methods initiated by I. M. Gelfand, we provide a sufficient condition for the irreducibility of these representations.
Energy quantization for Yamabe's problem in conformal dimension.
Engel structures with trivial characteristic foliations.
Engouffrement symplectique et intersections lagrangiennes.
Entire Spacelike Hypersurfaces on Constant Mean Curvature in Minkowski Space.
Entire spacelike radial graphs in the Minkowski space, asymptotic to the light-cone, with prescribed scalar curvature
Entropies et rigidité des espaces localement symétriques de courbure strictement.
Entropy and complexity of a path in sub-riemannian geometry
We characterize the geometry of a path in a sub-riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset of a metric space is the minimum number of balls of a given radius needed to cover . It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-riemannian manifold as the infimum of the lengths of all trajectories contained in an -neighborhood of the path,...
Entropy and complexity of a path in sub-Riemannian geometry
We characterize the geometry of a path in a sub-Riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset A of a metric space is the minimum number of balls of a given radius ε needed to cover A. It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-Riemannian manifold as the infimum of the lengths of all trajectories contained in an ε-neighborhood of the path,...
Entropy of eigenfunctions of the Laplacian in dimension 2
We study asymptotic properties of eigenfunctions of the Laplacian on compact Riemannian surfaces of Anosov type (for instance negatively curved surfaces). More precisely, we give an answer to a question of Anantharaman and Nonnenmacher [4] by proving that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. (This text has been written for the proceedings of the Journées EDP (Port d’Albret-June, 7-11 2010))
Entropy of Geodesic Flow and Exponent of Convergence of Some Dirichlet Series.
Enveloppe galoisienne d'une application rationnelle de P1.
In 2001, B. Malgrange defines the D-envelope or galoisian envelope of an analytical dynamical system. Roughly speaking, this is the algebraic hull of the dynamical system. In this short article, the D-envelope of a rational map R: P1 --> P1 is computed. The rational maps characterised by a finitness property of their D-envelope appear to be the integrable ones.