References
- Anderson G. Vamanamurthy M. Vuorinen M. 1997 Conformal Invariants, Inequalities, and Quasiconformal Maps. New York A Wiley-Interscience Publ
- Barbilian , D. 1934 . Incorporation of Lobachevsky's metric in certain general metrics of Jordan domains . Gasopis Matematiky a Fysiky , 5
- Beardon A. 1995 The Geometry of Discrete Groups. Springer New York
- Beardon A. 1998 The Apollonian metric of a domain in, Quasiconformal mappings and analysis In: F.W. Gehring P. Duren, J. Heinonen, B. Osgood and B. Palka (Eds.) A Collection of Papers Honoring pp. 91–108 Springer New York
- Chakerian G.D. Groemer H. 1983 In: P. Gruber and J. Wills (Eds.) Convex Bodies of Constant Width, Convexity and its Applications pp. 49–96 Birkhäuser Basel
- Eggleston H.C. 1958 Convexity. Cambridge University Press Cambridge
- Gardner R.J. 1995 Geometric Tomography. Cambridge University Press Cambridge
- Gehring , F.W. 1962 . Rings and quasiconformal mappings in space . Trans. Amer. Math. Soc. , 103 : 353 – 393 .
- Gehring , F.W. and Hag , K. 1999 . Bounds for the hyperbolic distance in a quasidisk . Ann. Univ. Mariae Curie-Skłodowska Sect. (A) , 53 : 67 – 72 .
- Gehring , F.W. and Hag , K. 2000 . The Apollonian metric and quasiconformal mappings . Contemp. Math. , 256 : 143 – 163 .
- Gehring , F.W. and Osgood , B.G. 1979 . Uniform domains and the quasihyperbolic metric . J. d’Analyse Math. , 36 : 50 – 74 .
- Gehring , F.W. and Palka , B.P. 1976 . Quasiconformally homogeneous domains . J. d’Analyse Math. , 30 : 172 – 199 .
- Hästö P. 2000 The Apollonian metric: general estimates preprint
- Hästö P. 2002 Sharp estimates of the Apollonian metric preprint
- Hästö P. 2002 Uniformity and quasiconvexity of the Apollonian metric preprint
- Iwaniec T. Martin G. 2001 Geometric Function Theory and Nonlinear Analysis New York Oxford University Press
- Kelly , P.J. 1954 . Barbilian geometry and the Poincaré model . Amer. Math. Monthly , 61 : 311 – 319 .
- Reshetnyak , Yu. G. 1967 . Liouville's Theorem on conformal mappings under minimal regularity assumptions . Sibirsk. Mat. Zh. , 8 : 835 – 840 .
- Schneider R. 1993 Convex Bodies: The Brunn-Minkowski Theory Cambridge University Press Cambridge
- Seittenranta , P. 1999 . Möbius-invariant metrics . Proc. Cambridge Philos. Soc. , 125 : 511 – 533 .