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    The Spherical Boundary and Volume Growth


    Buckley, Stephen M. and Kokkendorff, Simon L. (2012) The Spherical Boundary and Volume Growth. International Scholarly Research Network: ISRN Geometry (484312).

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    Abstract

    We consider the spherical boundary, a conformal boundary using a special class of conformal distortions. We prove that certain bounds on volume growth of suitable metric measure spaces imply that the spherical boundary is “small” �in cardinality or dimension� and give examples to show that the reverse implications fail. We also show that the spherical boundary of an annular convex proper length space consists of a single point. This result applies to l2-products of length spaces, since we prove that a natural metric, generalizing such “norm-like” product metrics on a �possibly infinite� product of unbounded length spaces, is annular convex
    Item Type: Article
    Keywords: Spherical Boundary; Volume Growth;
    Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 3885
    Depositing User: Prof. Stephen Buckley
    Date Deposited: 21 Sep 2012 10:43
    Journal or Publication Title: International Scholarly Research Network: ISRN Geometry
    Refereed: Yes
    Related URLs:
    URI: https://mural.maynoothuniversity.ie/id/eprint/3885
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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