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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: | |
| 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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