Rigidity of infinite (circle) packings
HTML articles powered by AMS MathViewer
- by Oded Schramm
- J. Amer. Math. Soc. 4 (1991), 127-149
- DOI: https://doi.org/10.1090/S0894-0347-1991-1076089-9
- PDF | Request permission
References
- E. M. Andreev, Convex polyhedra in Lobačevskiĭ spaces, Mat. Sb. (N.S.) 81 (123) (1970), 445–478 (Russian). MR 0259734
- E. M. Andreev, Convex polyhedra of finite volume in Lobačevskiĭ space, Mat. Sb. (N.S.) 83 (125) (1970), 256–260 (Russian). MR 0273510
- Imre Bárány, Zoltán Füredi, and János Pach, Discrete convex functions and proof of the six circle conjecture of Fejes Tóth, Canad. J. Math. 36 (1984), no. 3, 569–576. MR 752985, DOI 10.4153/CJM-1984-035-1
- Ithiel Carter and Burt Rodin, An inverse problem for circle packing and conformal mapping, Trans. Amer. Math. Soc. 334 (1992), no. 2, 861–875. MR 1081937, DOI 10.1090/S0002-9947-1992-1081937-X
- Zheng-Xu He, An estimate for hexagonal circle packings, J. Differential Geom. 33 (1991), no. 2, 395–412. MR 1094463
- Zheng-Xu He, Solving Beltrami equations by circle packing, Trans. Amer. Math. Soc. 322 (1990), no. 2, 657–670. MR 974518, DOI 10.1090/S0002-9947-1990-0974518-5
- Burt Rodin, Schwarz’s lemma for circle packings, Invent. Math. 89 (1987), no. 2, 271–289. MR 894380, DOI 10.1007/BF01389079
- Burt Rodin, Schwarz’s lemma for circle packings. II, J. Differential Geom. 30 (1989), no. 2, 539–554. MR 1010171
- Burt Rodin and Dennis Sullivan, The convergence of circle packings to the Riemann mapping, J. Differential Geom. 26 (1987), no. 2, 349–360. MR 906396 O. Schramm, Packing two-dimensional bodies with prescribed combinatorics and applications to the construction of conformal and quasiconformal mappings, Ph.D. thesis, Princeton, 1990. —, Uniqueness and existence of packings with specified combinatorics, Israel J. Math. (to appear).
- Kenneth Stephenson, Circle packings in the approximation of conformal mappings, Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 2, 407–415. MR 1049434, DOI 10.1090/S0273-0979-1990-15946-4 W. P. Thurston, The geometry and topology of $3$-manifolds, Princeton Univ. Lecture Notes, Princeton, NJ. —, The finite Riemann mapping theorem, invited talk at the International Symposium in Celebration of the Proof of the Bieberbach Conjecture, Purdue University, March 1985.
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: J. Amer. Math. Soc. 4 (1991), 127-149
- MSC: Primary 52C15; Secondary 30C65
- DOI: https://doi.org/10.1090/S0894-0347-1991-1076089-9
- MathSciNet review: 1076089