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TUBES IN SINGULAR SPACES OF NONPOSITIVE CURVATURE

  • Chai, Young-Do (Department of Mathematics Sungkyunkwan University) ;
  • Lee, Doo-Hann (Department of Mathematics Sungkyunkwan University)
  • Published : 2006.09.30

Abstract

In this paper, we estimate area of tube in a CBA(0)-space with extendible geodesics. As its application, we obtain an upper bound of systole in a nonsimply connected space of nonpositive curvature. Also, we determine a relative growth of a ball in a CBA(0)-space to the corresponding ball in Euclidean plane.

Keywords

References

  1. A. D. Alexandrov, A theorem on triangles in a metric space and some of its applications, Trudy Mat. Inst. Steklov. 38 (1951), 5-23
  2. A. D. Alexandrov, Uber eine verallgemeinerung der Riemannschen geometrie, Schr. Forschungs Inst. Math. 1 (1957) 33-84
  3. W. Ballmann, Lectures on spaces of nonpositive curvature, DMV Seminar, Band 25, Basel: Birkhauser, 1995
  4. C. Bavard, Inegalite isosystolique pour la bouteille de Klein, Math. Ann. 274 (1986), no. 3, 439-441 https://doi.org/10.1007/BF01457227
  5. Ju. D. Burago and V. A. Zalgaller, Geometric inequalities, Nauka : Leningrad, 1980
  6. L. Cesari, Surface area, Princeton Univ. Press, Princeton, New Jersey, 1956
  7. C. B. Croke, Area and the length of the shortest closed geodesic, J. Differential Geom. 27 (1988), no. 1, 1-21 https://doi.org/10.4310/jdg/1214441646
  8. A. Gray, Tubes, Addison-Wesley Pub., 1990
  9. J. J. Hebda, Some lower bounds for the area of surfaces, Invent. Math. 65 (1981/82), no. 3, 485-490 https://doi.org/10.1007/BF01396632
  10. C. Mese, Some properties of minimal surfaces in singular spaces, Trans. Amer. Math. Soc. 352 (2000), no. 9, 3957-3969 https://doi.org/10.1090/S0002-9947-00-02481-8
  11. K. Nagano, A Sphere theorem for 2-dimensional CAT(1)-spaces, Pacific J. Math. 206 (2002), no. 2, 401-423 https://doi.org/10.2140/pjm.2002.206.401
  12. I. G. Nikolaev, Solution of Plateau's problem in spaces of curvature no greater than k, Siberian Math. J. 20 (1979), 246-252 https://doi.org/10.1007/BF00970031

Cited by

  1. A NOTE ON SURFACES IN THE NORMAL BUNDLE OF A CURVE vol.27, pp.2, 2014, https://doi.org/10.14403/jcms.2014.27.2.211