The Spherical Boundary and Volume Growth
Joint Authors
Kokkendorff, Simon L.
Buckley, Stephen M.
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-03-26
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Buckley, Stephen M.& Kokkendorff, Simon L.. 2012. The Spherical Boundary and Volume Growth. ISRN Geometry،Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-475281
Modern Language Association (MLA)
Buckley, Stephen M.& Kokkendorff, Simon L.. The Spherical Boundary and Volume Growth. ISRN Geometry No. 2012 (2012), pp.1-13.
https://search.emarefa.net/detail/BIM-475281
American Medical Association (AMA)
Buckley, Stephen M.& Kokkendorff, Simon L.. The Spherical Boundary and Volume Growth. ISRN Geometry. 2012. Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-475281
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-475281