Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A LOWER BOUND FOR AREA OF COMPACT SINGULAR SURFACES OF NONPOSITIVE CURVATURE

  • Chai, Young-Do (Department of Mathematics Sungkyunkwan University) ;
  • Lee, Doo-Hann (Department of Mathematics Sungkyunkwan University)
  • Published : 2007.02.28
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Abstract

In this paper, we obtain some lower bounds for area of non-simply connected compact singular surfaces of nonpositive curvature. One inequality involves systole and area of the surface.

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References

  1. A. D. Alexandrov, A theorem on triangles in a metric space and some of its applications, Tr. Mat. Inst. Akad. Nauk SSSR 38 (1951), 5-23
  2. C. Bavard, Inegalite isosystolique pour la bouteille de Klein, Math. Ann. 274 (1986), no. 3, 439-441 https://doi.org/10.1007/BF01457227
  3. Y. D. Burago and V. A. Zalgaller, Geometric inequalities, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 110 (1981), 235-236
  4. S. Buyalo, Lectures on space of curvature bounded from above III, spring semester 1994/95 a.y. University of Illinois at Urbana Champaign.
  5. M. Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983), no. 1, 1-147 https://doi.org/10.4310/jdg/1214509283
  6. 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
  7. K. Nagano, A volume convergence theorem for Alexandrov spaces with curvature bounded above, Math. Z. 241 (2002), no. 1, 127-163 https://doi.org/10.1007/s002090100409
  8. P. M. Pu, Some inequalities in certain nonorientable Riemannian manifolds, Pacific J. Math. 2 (1952), 55-71 https://doi.org/10.2140/pjm.1952.2.55

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