Sur des problèmes de la géométrie systolique

Florent Balacheff

Séminaire de théorie spectrale et géométrie (2003-2004)

  • Volume: 22, page 71-82
  • ISSN: 1624-5458

How to cite

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Balacheff, Florent. "Sur des problèmes de la géométrie systolique." Séminaire de théorie spectrale et géométrie 22 (2003-2004): 71-82. <http://eudml.org/doc/114486>.

@article{Balacheff2003-2004,
author = {Balacheff, Florent},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {systole; geodesic loop; systolic inequality},
language = {fre},
pages = {71-82},
publisher = {Institut Fourier},
title = {Sur des problèmes de la géométrie systolique},
url = {http://eudml.org/doc/114486},
volume = {22},
year = {2003-2004},
}

TY - JOUR
AU - Balacheff, Florent
TI - Sur des problèmes de la géométrie systolique
JO - Séminaire de théorie spectrale et géométrie
PY - 2003-2004
PB - Institut Fourier
VL - 22
SP - 71
EP - 82
LA - fre
KW - systole; geodesic loop; systolic inequality
UR - http://eudml.org/doc/114486
ER -

References

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  2. [2] BAVARD, C., Inégalité isosystolique pour la bouteille de Klein, Math. Ann., 274 ( 1986), 439-441. Zbl0578.53032MR842624
  3. [3] BIRKHOFF, G., Dynamicals Systems with two degrees of freedom, Trans. Amer. Math. Soc, 18 ( 1917), 199-300. Zbl46.1174.01MR1501070JFM46.1174.01
  4. [4] BOLLOBÁS, B. & SZEMERÉDI, E., Girth of sparse graphs, J. Graph Theory, 39 ( 2002), 194-200. Zbl1176.05038MR1883596
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  7. [7] CAIABI, C. & CAO, J., Simple closed geodesics on convex surfaces, J. Differential Geometry, 36 ( 1992), 517-549. Zbl0768.53019MR1189495
  8. [8] CROKE, C., Area and the length of the shortest closed geodesic, J. Differential Geometry, 27 ( 1988), 1-22. Zbl0642.53045MR918453
  9. [9] GROMOV, M., Filling Riemannian Manifolds, J. Differential Geometry, 18 ( 1983), 1-147. Zbl0515.53037MR697984
  10. [10] GROMOV, M., Systoles and intersystolic inequalities, Actes de la Table Ronde de Géométrie Différentielle, Sem. Congr., 1 ( 1996), Soc Math. France, 291-362. Zbl0877.53002MR1427763
  11. [11] HIRSCH, M., Differential Topology, Graduate Texts in Math., Springer Verlag New-York, 33, 1976. Zbl0356.57001MR448362
  12. [12] KLINGENBERG, W., Lectures on closed geodesics, Grundlehren Math. Wiss., 230, Springer Verlag, Berlin, 1978. Zbl0397.58018MR478069
  13. [13] KODANI, S., On two dimensional isosystolic inequalities, Kodai Math. J., 10 ( 1987), 314-327. Zbl0642.53042MR929991
  14. [14] MAEDA, M., The length of a closed geodesic on a compact surface, Kyushu J. Math., 48-1 ( 1994), 9-18. Zbl0818.53064MR1269063
  15. [15] NABUTOVSKY, A. & ROTMAN, R., The length of the shortest closed geodesic on a 2-dimensional sphere, Int. Math. Res. Not., 23 ( 2002), 1211-1222. Zbl1003.53030MR1903953
  16. [16] NABUTOVSKY, A. & ROTMAN, R., Upper bounds on the length ofa shortest closed geodesic and quantitative Hurewicz theorem,J. Eur. Math. Soc, 5- 3 ( 2003), 203-244. Zbl1039.53042MR2002213
  17. [17] NABUTOVSKY, A. & ROTMAN, R., Volume, Diameter and the minimal mass of a stationnary 1-cycle, arXiv :Math.DG/0201269, 2002. Zbl1073.53057MR2084979
  18. [18] PU, R., Some inequalities in certain nonorientable Riemannian manifolds, Pacific J. Math., 2 ( 1952), 55-72. Zbl0046.39902MR48886
  19. [19] SABOURAU, S., Filling radius and short closed geodesic of the sphere, Bull. SMF, 132 ( 2004), 105-136. Zbl1064.53020MR2075918
  20. [20] SABOURAU, S., Global and local volume bounds and the shortest geodesic loop, à paraître dans Communications in Analysis and Geometry. Zbl1075.53030

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