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We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.
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.
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