Abstract: a foliation of a compact manifold? has a complete Riemannian metric determined up to quasi-isometry. In fact, since a quasi-isometry is by definition a diffeomorphism with global bounds on how much it can stretch or shrink a tangent vector, any two metrics on the manifold are quasi-isometric and the same must hold for the metrics they induce on the leaf. From this point of view it is interesting to ask: what do leaves of foliations of compact manifolds look like? We will prove here, for example, that the quasi- isometry types of the “Jacob’...
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Topics: 
Pure mathematics
Mathematical analysis