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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Minimal leaves in foliations


Author: Daniel M. Cass
Journal: Trans. Amer. Math. Soc. 287 (1985), 201-213
MSC: Primary 57R30; Secondary 53C12
DOI: https://doi.org/10.1090/S0002-9947-1985-0766214-2
MathSciNet review: 766214
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Abstract: The paper defines a property of open Riemannian manifolds, called quasi-homogeneity. This property is quasi-isometry invariant and is shown to hold for any manifold which appears as a minimal leaf in a foliation. Examples are given of surfaces which are not quasi-homogeneous. One such is the well-known noncompact leaf of Reeb's foliation of $ {S^3}$. These surfaces have bounded geometry.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0766214-2
Keywords: Dilation, quasi-isometry class, minimal set of leaves, recurrent
Article copyright: © Copyright 1985 American Mathematical Society