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The boundary of a Busemann space
Author(s):
Philip
K.
Hotchkiss
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1903-1912.
MSC (1991):
Primary 20F32
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Abstract:
Let  be a proper Busemann space. Then there is a well defined boundary,  , for  . Moreover, if  is (Gromov) hyperbolic (resp. non-positively curved), then this boundary is homeomorphic to the hyperbolic (resp. non-positively curved) boundary.
References:
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- B. H. Bowditch, Minkowskian Subspaces of Non-positively Curved Subspaces, preprint.
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- M. Bridson, Geodesics and Curvature in Metric Simplicial Complexes, Group Theory from a Geometrical Viewpoint (E. Ghys, A. Haefliger, and A. Verjovsky, eds.), Proceedings of ICTP, Trieste, Italy, World Scientific, 1991, pp. 373-463. MR 94c:57040
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- E. Freden, Negatively Curved Groups have the Convergence Property. I, II,Ann. Acad. Sci. Fenn. Math. 20 (1995), 333-348; 21 (1996), 133-150. MR 96g:20054; CMP 96:08
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- E. Ghys and P. de la Harpe (eds.), Sur le Groupes Hyperboliques d'après Mikhael Gromov, Progress in Mathematics 83, Birkhäuser, Boston, 1990. MR 92f:53050
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- J. Munkres, Topology: A First Course, Prentice Hall, Englewood Cliffs, 1975. MR 57:4063
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- F. Paulin, Constructions of Hyperbolic Groups via Hyperbolization of Polyhedra, Group Theory from a Geometrical Viewpoint (E. Ghys, A. Haefliger, and A. Verjovsky, eds.), Proceedings of ICTP, Trieste, Italy, World Scientific, 1991, pp. 313-372. MR 93d:57005
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- E. Swenson, Negatively Curved Groups and Related Topics, PhD Thesis, Brigham Young University (1993).
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Additional Information:
Philip
K.
Hotchkiss
Affiliation:
Department of Mathematics, The University of St. Thomas, St. Paul, Minnesota 55015
Email:
pkhotchkiss@stthomas.edu
DOI:
10.1090/S0002-9939-97-04166-X
PII:
S 0002-9939(97)04166-X
Keywords:
Busemann space,
geodesic,
proper
Received by editor(s):
November 19, 1995
Communicated by:
James E. West
Copyright of article:
Copyright
1997,
American Mathematical Society
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