Skip to main content
Log in

Un principe variationnel pour les empilements de cercles

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Bibliographie

  • [AL] Ahlfors, L.: Lectures on quasi-conformal mappings. Van Nostrand 1982

  • [AN] Andreev, E.M.. On convex polyhedra in Lobaĉeskiî spaces. Mat. USSR Sbornik10, 413–440 (1970)

    Article  Google Scholar 

  • [BE] Berge, C.: Graphes et hypergraphes. Dunod 1973

  • [BN] Beardon, A.: The geometry of discrete groups. Berlin Heidelberg New York: Springer 1983

    Book  MATH  Google Scholar 

  • [CH] Choquet, G.: Sur un type de transformation analytique... défini au moyen de fonctions harmoniques. Bull. Sci. Math.,69, 156–165 (1945)

    MathSciNet  MATH  Google Scholar 

  • [CV 1] Colin de Verdière, Y.: Empilements de cercles: convergence d'une méthode de points fixe. Forum Math.1, 395–402 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  • [CV 2] Colin de Verdière, Y.: Déformations géodésiques des triangulations de surfaces, Prépublication de l'Institut Fourier n0 161 (1990)

  • [FY] Fary, I.: On straight line representation of planar graphs. Acta Sci. Math. SzegedII, 229–233 (1948)

    MathSciNet  MATH  Google Scholar 

  • [OPS] Osgood, Phillips, Sarnak: Extremals of determinants of Laplacians. J. Funct. Anal.80, 148–212 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  • [RS] Rodin, B., Sullivan, D.: The convergence ofcircle packings to the Riemann mapping. J. Diff. Geom.26, 349–360 (1987)

    MathSciNet  MATH  Google Scholar 

  • [SM] Schramm, O.: Existence and uniqueness of packings with specified combinatorics. Preprint UCSD (a paraitre, 1990)

  • [ST] Stephenson, K.: Circle packings in the approximations of conformal mappings. Bull. AMS123, 407–415 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  • [S-Y] Schoen, R., Yau, S.T.: On univalent harmonic maps between surfaces. Invent. Math.44, 265–278 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  • [TH] Thurston, W.: The geometry and topology of three-manifolds. Princeton Notes, chap. 13, 1978

  • [TO 1] Thomassen, C.: Planarity and duality of finite and infinite graphs. J. Comb. TheoryB 29, 244–271 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  • [TO 2] Thomassen, C.: Plane representations of graphs. In: Progress in graph theory, pp. 43–69. Academic press 1984

  • [TU] Tutte, W.: How to draw a graph. Proc. Lond. Math. Soc.13, 743–768 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  • [TV] Troyanov, M.: Les surfaces euclidiennes à singularités coniques. Ens. Math.32, 79–94 (1986)

    MathSciNet  MATH  Google Scholar 

  • [ZH] Zheng,-Xu He: An estimate for hexagonal circle packings, J. Diff. Geom. (à paraître 1990)

Download references

Author information

Authors and Affiliations

Authors

Additional information

Oblatum 16-XI-1990

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Verdière, Y.C. Un principe variationnel pour les empilements de cercles. Invent. math. 104, 655–669 (1991). https://doi.org/10.1007/BF01245096

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01245096

Navigation