Rigidity of infinite (circle) packings

Author:
Oded Schramm

Journal:
J. Amer. Math. Soc. **4** (1991), 127-149

MSC:
Primary 52C15; Secondary 30C65

MathSciNet review:
1076089

Full-text PDF Free Access

References | Similar Articles | Additional Information

**[An1]**E. M. Andreev,*Convex polyhedra in Lobačevskiĭ spaces*, Mat. Sb. (N.S.)**81 (123)**(1970), 445–478 (Russian). MR**0259734****[An2]**E. M. Andreev,*Convex polyhedra of finite volume in Lobačevskiĭ space*, Mat. Sb. (N.S.)**83 (125)**(1970), 256–260 (Russian). MR**0273510****[BFP]**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**, 10.4153/CJM-1984-035-1**[CR]**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**, 10.1090/S0002-9947-1992-1081937-X**[He1]**Zheng-Xu He,*An estimate for hexagonal circle packings*, J. Differential Geom.**33**(1991), no. 2, 395–412. MR**1094463****[He2]**Zheng-Xu He,*Solving Beltrami equations by circle packing*, Trans. Amer. Math. Soc.**322**(1990), no. 2, 657–670. MR**974518**, 10.1090/S0002-9947-1990-0974518-5**[Ro1]**Burt Rodin,*Schwarz’s lemma for circle packings*, Invent. Math.**89**(1987), no. 2, 271–289. MR**894380**, 10.1007/BF01389079**[Ro2]**Burt Rodin,*Schwarz’s lemma for circle packings. II*, J. Differential Geom.**30**(1989), no. 2, 539–554. MR**1010171****[RS]**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****[Sch1]**O. Schramm,*Packing two-dimensional bodies with prescribed combinatorics and applications to the construction of conformal and quasiconformal mappings*, Ph.D. thesis, Princeton, 1990.**[Sch2]**-,*Uniqueness and existence of packings with specified combinatorics*, Israel J. Math. (to appear).**[Ste]**Kenneth Stephenson,*Circle packings in the approximation of conformal mappings*, Bull. Amer. Math. Soc. (N.S.)**23**(1990), no. 2, 407–415. MR**1049434**, 10.1090/S0273-0979-1990-15946-4**[Th1]**W. P. Thurston,*The geometry and topology of**-manifolds*, Princeton Univ. Lecture Notes, Princeton, NJ.**[Th2]**-,*The finite Riemann mapping theorem*, invited talk at the International Symposium in Celebration of the Proof of the Bieberbach Conjecture, Purdue University, March 1985.

Retrieve articles in *Journal of the American Mathematical Society*
with MSC:
52C15,
30C65

Retrieve articles in all journals with MSC: 52C15, 30C65

Additional Information

DOI:
http://dx.doi.org/10.1090/S0894-0347-1991-1076089-9

Article copyright:
© Copyright 1991
American Mathematical Society