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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: | |
| 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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