Busemann points of infinite graphs
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- by Corran Webster and Adam Winchester PDF
- Trans. Amer. Math. Soc. 358 (2006), 4209-4224 Request permission
Abstract:
We provide a geometric condition which determines whether or not every point on the metric boundary of a graph with the standard path metric is a Busemann point, that is, it is the limit point of a geodesic ray. We apply this and a related condition to investigate the structure of the metric boundary of Cayley graphs. We show that groups such as the braid group and the discrete Heisenberg group have boundary points of the Cayley graph which are not Busemann points when equipped with their usual generators.References
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Additional Information
- Corran Webster
- Affiliation: Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, Nevada 89154
- Email: cwebster@unlv.nevada.edu
- Adam Winchester
- Affiliation: Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, Nevada 89154
- Address at time of publication: Department of Mathematics, University of California–Los Angeles, Box 951555, Los Angeles, California 90095-1555
- Email: lagwadam@math.ucla.edu
- Received by editor(s): September 5, 2003
- Received by editor(s) in revised form: September 28, 2004
- Published electronically: April 11, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 4209-4224
- MSC (2000): Primary 20F65; Secondary 46L87, 53C23
- DOI: https://doi.org/10.1090/S0002-9947-06-03877-3
- MathSciNet review: 2219016