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Dans cet article on étudie les -modules dont le support singulier est un croisement normal dans , par l’intermédiaire de la catégorie équivalente de faisceaux pervers. On montre qu’ils sont caractérisés, à isomorphisme près, par la donnée suivante : un hypercube constitué par des espaces vectoriels de dimension finie indexés par les parties de , et des applications linéaires soumises à certaines conditions de commutativité et d’inversibilité. Ce résultat est exprimé sous forme d’une équivalence...
We study the propagation of microlocal analytic singularities for the microdifferential equations with conical refraction studied by R. Melrose and G. Uhlmann. We transform the equations to a simple canonical form 2-microlocaly through quantized bicanonical transformations by Y. Laurent.
denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on is harmonic if and only if it is the projection of a measure on the unit tangent bundle of which is invariant under both the geodesic and the horocycle flows.
Let be a principal fiber bundle and an associated fiber bundle. Our interest is to study the harmonic sections of the projection of into . Our first purpose is give a characterization of harmonic sections of into regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of .
For , let be a bounded smooth domain and a compact smooth Riemannian manifold without boundary. Suppose that is a sequence of weak solutions in the critical dimension to the perturbed -polyharmonic maps with in and weakly in . Then is an -polyharmonic map. In particular, the space of -polyharmonic maps is sequentially compact for the weak- topology.