Remarks on sphere packings, clusters and Hales Ferguson theorem

Jean-Louis Verger-Gaugry

Séminaire de théorie spectrale et géométrie (2000-2001)

  • Volume: 19, page 165-177
  • ISSN: 1624-5458

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Verger-Gaugry, Jean-Louis. "Remarks on sphere packings, clusters and Hales Ferguson theorem." Séminaire de théorie spectrale et géométrie 19 (2000-2001): 165-177. <http://eudml.org/doc/114455>.

@article{Verger2000-2001,
author = {Verger-Gaugry, Jean-Louis},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {density; aperiodic packings; Hales Ferguson theorem; sphere packings},
language = {eng},
pages = {165-177},
publisher = {Institut Fourier},
title = {Remarks on sphere packings, clusters and Hales Ferguson theorem},
url = {http://eudml.org/doc/114455},
volume = {19},
year = {2000-2001},
}

TY - JOUR
AU - Verger-Gaugry, Jean-Louis
TI - Remarks on sphere packings, clusters and Hales Ferguson theorem
JO - Séminaire de théorie spectrale et géométrie
PY - 2000-2001
PB - Institut Fourier
VL - 19
SP - 165
EP - 177
LA - eng
KW - density; aperiodic packings; Hales Ferguson theorem; sphere packings
UR - http://eudml.org/doc/114455
ER -

References

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  1. [A] H. AKROUT, Systoles généralisées, preprint, 2001. 
  2. [B] C. BAVARD, Systole et invariant d'Hermite, J. reine und angew. Math., 482, ( 1997), 93-120. Zbl1011.53035MR1427658
  3. [CS] J.H. CONWAY AND N. J. A. SLOANE, Sphere packings, lattices and groups, Springer-Verlag, 1988. Zbl0634.52002MR920369
  4. [FT] L. FEJES-TÓTH, Über einen geometrischen Satz, Math. Z., 46, ( 1940), 79-83. MR1587
  5. [F] S.L.P. FERGUSON, Sphere packings V, preprint, 1999.. MR1707318
  6. [GL] P.M. GRUBERAND C.G. LERKKERKERKER, Geometry of Numbers, North-Holland, ( 1987). Zbl0611.10017MR1242995
  7. [H] T.C. HALES, Cannonballs and Honeycombs, Notices of the AMS, 47, n° 4, ( 2000), 440-449. Zbl1040.52012MR1745624
  8. [H2] T.C. HALES, The status of the Kepler conjecture, The Mathematical Intelligences 16, n° 3, ( 1994), 44-58. Zbl0844.52018MR1281754
  9. [H3] T.C. HALES, Sphere packings 1, Disc. Comp. Geom. 17, ( 1997), 1-51. Zbl0883.52012MR1418278
  10. [H4] T.C. HALES, Sphere packings II, Disc. Comp. Geom. 18, ( 1997), 135-149. Zbl0883.52013MR1455511
  11. [Hs] W.-Y. HSIANG, On the sphere packing problem and the proof of Kepler's conjecture, Int. J. Math., 93, ( 1993), 739-831. Zbl0844.52017MR1245351
  12. [M] J. MARTINET, Les réseaux parfaits des espaces euclidiens, Masson, 1996. Zbl0869.11056MR1434803
  13. [MVG] G. MURAZ AND J.-L. VERGER-GAUGRY, A compactness theorem for the set of uniformly discrete sets and its subsets: lattices, clusters, model sets and Delone sets, preprint, 2001. 
  14. [O] J. OESTERLÉ, Densité maximale des empilements de sphères en dimension 3 [d'après Thomas C. Hales et Samuel P. Ferguson], Séminaire Bourbaki, n° 863, ( 1998-99), 405-413. Zbl0958.52022MR1772681
  15. [O1] J. OESTERLÉ, Empilements de sphères, Séminaire Bourbaki, n° 727, ( 1989-90), 375-397; SMF Astérisque 189-190, ( 1990). Zbl0731.52005MR1099882
  16. [R] C.A. ROGERS, Packing and covering, Cambridge University Press, 1964. Zbl0176.51401MR172183
  17. [T] A. THUE, Über die dichteste Zusammenstellung von kongruenten Kreisen in einer Ebene, Skr. Vidensk-Selsk., Christ. N° 1, ( 1910), 1-9. Zbl41.0550.02JFM41.0550.02
  18. [VG] J.-L. VERGER-GAUGRY, On a generalization of the Hermite constant, Periodica Mathematica Hungarica, 34, ( 1997), 153-164. Zbl0880.52013MR1608302

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