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The Apollonius problem in four-dimensional Laguerre planes

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Abstract

The number of circles of a four-dimensional locally compact Laguerre plane touching three given circles or points depends only on the given geometric configuration but not on the Laguerre plane.

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References

  1. Ahlfors, L.V. undSario, L.: Riemann Surfaces, Princeton University Press, Princeton, 1960

    Google Scholar 

  2. Brouwer, L.E.J.: Über die periodischen Transformationen der Kugel, Math. Ann.80 (1919), 39–41

    Google Scholar 

  3. Browder, F.E.: Covering spaces, fibre spaces, and local homeomorphisms, Duke Math. J.21 (1954), 329–336

    Google Scholar 

  4. Buchanan, T., Hähl, H. undLöwen, R.: Topologische Ovale, Geom. Dedicata9 (1980), 401–424

    Google Scholar 

  5. Forst, M.: Topologische 4-Gone, Mitt. d. Math. Sem. Gießen147 (1981), 65–129

    Google Scholar 

  6. Groh, H.: Topologische Laguerre-Ebenen I, Abh. Math. Sem. Univ. Hamburg32 (1968), 216–231

    Google Scholar 

  7. Groh, H.: Topologische Laguerre-Ebenen II, Abh. Math. Sem. Univ. Hamburg34 (1969), 11–21

    Google Scholar 

  8. Kerékjartó B. von: Über die periodischen Transformationsgruppen der Kreisscheibe und der Kugelfläche, Math. Ann.80 (1919), 36–38

    Google Scholar 

  9. Łysko, J.M.: Some theorems concerning finite dimensional homogeneous ANR-spaces, Bull. Acad. Polon. Sci.24 (1976), 491–496

    Google Scholar 

  10. Schroth, A.E.: Three Dimensional Quadrangles and Flat Laguerre Planes, Geom. Dedicata36 (1990), 365–373

    Google Scholar 

  11. Schroth, A.E.: The Appolonius Problem in Flat Laguerre Planes, J. Geom.42 (1991), 141–147

    Google Scholar 

  12. Schroth, A.E.: Topologische Laguerreebenen und topologische Vierecke, Dissertation, Braunschweig, 1992

  13. Schroth, A.E.: On the structure of topological n-gons, to appear in Simon Stevin

  14. Schroth, A.E.: Generalized quadrangles constructed from topological Laguerre planes, Geom. Dedicata46 (1993), 339–361

    Google Scholar 

  15. Schroth, A.E.: Topological antiregular Quadrangles, to appear in Results in Math.

  16. Tits. J.: Sur la trialité et certains groupes qui s'en déduisent, Publ. Math.: I.H.E.S.2 (1959), 13–60

    Google Scholar 

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  1. Institut für Analysis Abteilung für Topologie und Grundlagen der Analysis, Technische Universität, Pockelsstr. 14, D-38106, Braunschweig

    Andreas E. Schroth

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  1. Andreas E. Schroth
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Schroth, A.E. The Apollonius problem in four-dimensional Laguerre planes. J Geom 51, 138–149 (1994). https://doi.org/10.1007/BF01226863

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  • DOI: https://doi.org/10.1007/BF01226863

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