The Apollonian Metric : Uniformity and Quasiconvexity

@inproceedings{RhodesTheAM,
  title={The Apollonian Metric : Uniformity and Quasiconvexity},
  author={A Gayle Rhodes and P. Seittenranta and Frank Gehring and K. Hag}
}
In this paper we examine implications of a mapping being bilipschitz with respect to the Apollonian metric. The main results are improvements of results by Gehring and Hag which aim at describing Apollonian isometries. We also derive results on quasi-isotropy and quasiconvexity of the Apollonian metric. 

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References

Publications referenced by this paper.
Showing 1-10 of 23 references

The Apollonian metric: geometry of comparison and bilipschitz domains. - Ph.D. Thesis (part)

  • P. A. Hästö
  • University of Helsinki,
  • 2003
Highly Influential
9 Excerpts

The Apollonian metric of a domain in R

  • A. F. Beardon
  • Quasiconformal Mappings and Analysis,
  • 1998
Highly Influential
4 Excerpts

Geometry of Discrete Groups

  • A. F. Beardon
  • Graduate Texts in Math
  • 1995
Highly Influential
4 Excerpts

The Apollonian metric, set of constant width and Möbius modulus of ring domains

  • Z. Ibragimov
  • Ph.D. Thesis,
  • 2002
2 Excerpts

Möbius-invariant metrics. - Math

  • P. Seittenranta
  • Proc. Cambridge Philos. Soc. 125,
  • 1999
2 Excerpts

The Apollonian metric and quasiconformal mappings

  • F. W. Gehring, K. Hag
  • In the Tradition of Ahlfors and Bers (Stony Brook…
  • 1998
5 Excerpts

An upper bound for the hyperbolic metric of a convex domain

  • A. G. Rhodes
  • Bull. London Math. Soc
  • 1997
1 Excerpt

Hyperbolic geometry and Barbilian spaces. - Istituto per la Ricerca di Base, Series of Monographs in Advanced Mathematics

  • Boskoff, W.-G
  • 1996
3 Excerpts

The free quasiworld. Freely quasiconformal and related maps in Banach spaces. - In: Quasiconformal Geometry and Dynamics (Lublin

  • J. Väisälä
  • Polish Acad. Sci., Warsaw,
  • 1996

The Apollonian metric of a domain in R n

  • A. F. Beardon
  • Geometry of Discrete Groups . - Graduate Texts in…
  • 1995

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