Einstein-Maxwell equation on four-dimensional homogeneous spaces.
Einstein-Weyl geometry, the Bach tensor and conformal scalar curvature.
Einstein-Weyl structures on lightlike hypersurfaces
We study Weyl structures on lightlike hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for ambient Lorentzian space ℝ1n+2 and a totally umbilical screen foliation, there is a strong interplay with the induced (Riemannian) Weyl-structure on the leaves.
Einstein-Yang Mills equations for gauge transformations of second order.
El polinomio de Poincaré-Hodge de un producto simétrico de variedades kählerianas compactas.
In this paper we compute the Poincaré-Hodge polynomial of a symmetric product of a compact kähler manifold, following the method used by Macdonald, in the topological case, to compute the Poincaré polynomial of a compact polyhedron, and we give some applications, in particular to the case of curves.
Electromagnetic dynamical systems.
Ellipsoids and hyperboloids with infinite foci
Elliptic functions in spherically symmetric solutions of Einstein's equations
Elliptic operators and higher signatures
Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov’s higher signatures on closed manifolds, - the problem of cut-and-paste invariance of Novikov’s higher signatures on closed manifolds, - the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.
Elliptic problems with integral diffusion
In this paper, we review several recent results dealing with elliptic equations with non local diffusion. More precisely, we investigate several problems involving the fractional laplacian. Finally, we present a conformally covariant operator and the associated singular and regular Yamabe problem.
Ellipticity of the symplectic twistor complex
For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections of certain infinite rank vector bundles defined over this manifold. The differential operators are symplectic analogues of the twistor operators known from Riemannian or Lorentzian spin geometry. It is known that the mentioned sequences form complexes if the symplectic...
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.