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Matematicheskie Trudy, 2007, Volume 10, Number 1, Pages 16–28 (Mi mt28)  
This article is cited in 4 scientific papers (total in 4 papers)

Geometry of Ideal Boundaries of Geodesic Spaces with Nonpositive Curvature in the Sense of Busemann

P. D. Andreev

M. V. Lomonosov Pomor State University
Full-text PDF (222 kB) Citations (4)
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Abstract: We establish relations between different approaches to the ideal closure of a geodesic metric space with nonpositive curvature in the sense of Busemann. We construct the counterexample showing that the Busemann ideal closure can differ from the geodesic closure.
Key words: geodesic, nonpositive curvature, Busemann space, horofunction, Busemann function, metric boundary, geodesic boundary, CAT(0)-space.
Received: 12.07.2005
English version:
Siberian Advances in Mathematics, 2008, Volume 18, Issue 2, Pages 95–102
DOI: https://doi.org/10.3103/S105513440802003X
Bibliographic databases:
UDC: 514.774.8
Language: Russian
Citation: P. D. Andreev, “Geometry of Ideal Boundaries of Geodesic Spaces with Nonpositive Curvature in the Sense of Busemann”, Mat. Tr., 10:1 (2007), 16–28; Siberian Adv. Math., 18:2 (2008), 95–102
Citation in format AMSBIB
\Bibitem{And07}
\by P.~D.~Andreev
\paper Geometry of Ideal Boundaries of Geodesic Spaces with Nonpositive Curvature in the Sense of Busemann
\jour Mat. Tr.
\yr 2007
\vol 10
\issue 1
\pages 16--28
\mathnet{http://mi.mathnet.ru/mt28}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2485365}
\transl
\jour Siberian Adv. Math.
\yr 2008
\vol 18
\issue 2
\pages 95--102
\crossref{https://doi.org/10.3103/S105513440802003X}
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  • https://www.mathnet.ru/eng/mt28
  • https://www.mathnet.ru/eng/mt/v10/i1/p16
    • This publication is cited in the following 4 articles:
    1. Andreev P., “The Cone Metric of a Busemann Space”, J. Geom., 109:1 (2018), UNSP 25  crossref  mathscinet  isi  scopus
    2. Piatek B., “On the Fixed Point Property For Nonexpansive Mappings in Hyperbolic Geodesic Spaces”, J. Nonlinear Convex Anal., 19:4 (2018), 571–582  mathscinet  isi
    3. Piatek B., “the Behavior of Fixed Point Free Nonexpansive Mappings in Geodesic Spaces”, J. Math. Anal. Appl., 445:1 (2017), 1071–1083  crossref  mathscinet  zmath  isi  scopus
    4. P. D. Andreev, “A. D. Alexandrov's problem for non-positively curved spaces in the sense of Busemann”, Russian Math. (Iz. VUZ), 54:9 (2010), 7–29  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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    Abstract page:589
    Full-text PDF :159
    References:77
    First page:1
     
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