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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;
Subjects: Science & Engineering > Mathematics
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
URI:

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