Gromov hyperbolicity of certain conformal invariant metrics

Annales Academiae Scientiarum Fennicae Mathematica

Volumn 32, Issue 1, 2007, Pages 279-288

  Lindén, Henri ^a  

^a UNIVERSITY OF HELSINKI   (Finland)

Author keywords

Conformal modulus; Ferrand's metric; Gromov hyperbolic; Modulus metric

Indexed keywords

EID: 42149126038     PISSN: 1239629X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. ANDERSON, G., M. VAMANAMURTHY, and M. VUORINEN: Conformal invariants, inequalities, and quasiconformal maps. - Canad. Math. Soc. Series of Monographs and Advanced Texts. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1997.
2. BONK, M., J. HEINONEN, and P. KOSKELA: Uniformizing Gromov hyperbolic spaces. - Astérisque 270, 2001, 1-99.
3. BONK, M., and O. SCHRAMM: Embeddings of Gromov hyperbolic spaces. - Geom. Funct. Anal. 10:2, 2000, 266-306.
4. BURAGO, D., Y. BURAGO, and S. IVANOV: A course in metric geometry. - Grad. Stud. Math. 33, AMS, Providence, RI, 2001.
5. COORNAERT, M., T. DELZANT, and A. P APADOPOULOS: Géométrie et théorie des groupes. - Lecture Notes in Math. 1441, Springer-Verlag, Berlin, 1990, (in French, English summary).
6. FERRAND, J.: Conformal capacity and extremal metrics. - Pacific J. Math. 180:1, 1997, 41-49.
7. GÁL, I. S.: Conformally invariant metrics and uniform structures. - Indag. Math. 22, 1960, 218-244.
8. G metrics. - Proc. Amer. Math. Soc. 134, 2006, 1137-1142.
9. LELONG-FERRAND, J.: Invariants conformes globaux sur les varietes riemanniennes. - J. Diff. Geom. 8, 1973, 487-510, (in French).
10. LEHTO O., and K. VIRTANEN: Quasiconformal mappings in the plane. - Grundlehren Math. Wiss. 126, 2nd edition, Springer-Verlag, Berlin-Heidelberg-New York, 1973.
11. MARTIO, O., and J. SARVAS: Injectivity theorems in plane and space. - Ann. Acad. Sci. Fenn. Ser. A I Math. 4, 1978/79, 383-401.
12. SEITTENRANTA, P.: Möbius-invariant metrics. - Math. Proc. Camb. Phil. Soc. 125, 1999, 511-533.
13. VÄISÄLÄ, J.: Lectures on n-dimensional quasiconformal mappings. - Lecture Notes in Math. 229, Springer-Verlag, Berlin-New York, 1971.
14. VÄISÄLÄ, J.: Gromov hyperbolic spaces. - Expo. Math. 23, 2005, 187-231.
15. VUORINEN, M.: Conformal geometry and quasiregular mappings. - Lecture Notes in Math. 1319, Springer-Verlag, Berlin, 1988.
16. VUORINEN, M.: Conformally invariant extremal problems and quasiconformal maps. - Quart. J. Math. Oxford Ser. (2) 43:172, 1992, 501-514.