Complete minimal hypersurfaces with prescribed asymptotics at infinity.
En utilisant une méthode dépendante du temps, nous démontrons la complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats. On introduit l'observable de vitesse asymptotique et on décrit son spectre (sous des hypothèses plus faibles que pour la complétude asymptotique). Les méthodes utilisées sont inspirées par celles de l'analyse du problème à deux corps en mécanique quantique.
There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a -valued function defined on the boundary of a bounded regular domain of . When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic map away from a codimension-2 minimal current minimizing the area within the homology...
This is an exposition of a general machinery developed by M. G. Eastwood, T. N. Bailey, C. R. Graham which analyses some real integral transforms using complex methods. The machinery deals with double fibrations complex manifold; totally real, real-analytic submanifold;...
We establish a composition calculus for Fourier integral operators associated with a class of smooth canonical relations . These canonical relations, which arise naturally in integral geometry, are such that : is a Whitney fold and : is a blow-down mapping. If , , then a class of pseudodifferential operators with singular symbols. From this follows boundedness of with a loss of 1/4 derivative.
Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of . Singularity classes containing bifurcation points with , are considered.