The topology of balls and Gromov hyperbolicity of Riemann surfaces

Differential Geometry and its Application

Volumn 21, Issue 3, 2004, Pages 317-335

  Portilla, Ana ^a   Rodríguez, José M ^a   Tourís, Eva ^a  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

Funnel; Gromov hyperbolicity; Puncture; Riemann surface

Indexed keywords

EID: 4644337720     PISSN: 09262245     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.difgeo.2004.05.006     Document Type: Article

References (29)

1. Alvarez V. Pestana D. Rodríguez J.M. Isoperimetric inequalities in Riemann surfaces of infinite type Rev. Mat. Iberoamericana 15 1999 353-427
2. Alvarez V. Rodríguez J.M. Yakubovich V.A. Subadditivity of p-harmonic "measure" on graphs Michigan Math. J. 49 2001 47-64
3. Bonk M. Heinonen J. Koskela P. Uniformizing Gromov hyperbolic spaces Astérisque 270 2001
4. Buser P. Geometry and Spectra of Compact Riemann Surfaces 1992 Birkhäuser Boston
5. Cantón A. Fernández J.L. Pestana D. Rodríguez J.M. On harmonic functions on trees Potential Anal. 15 2001 199-244
6. Chavel I. Eigenvalues in Riemannian Geometry 1984 Academic Press New York
7. Cheeger J. Finiteness theorems for Riemannian manifolds Amer. J. Math. 96 1970 61-74
8. Fernández J.L. Rodríguez J.M. The exponent of convergence of Riemann surfaces. Bass Riemann surfaces Ann. Acad. Sci. Fenn. Ser. AI 15 1990 165-183
9. Fernández J.L. Rodríguez J.M. Area growth and Green's function of Riemann surfaces Ark. Mat. 30 1992 83-92
10. Ghys E. de la Harpe P. Sur les Groupes Hyperboliques d'après Mikhael Gromov Progr. Math. vol. 83 1990 Birkhäuser Basel
11. Gromov M. Curvature, diameter and Betti numbers Comment. Math. Helv. 56 1981 179-195
12. Grove K. Petersen P. Bounding homotopy types by geometry Ann. of Math. 128 1988 195-206
13. Grove K. Petersen P. Wu J.Y. Invent. Math. 104 1991 221-222 Correction
14. Holopainen I. Soardi P.M. p-harmonic functions on graphs and manifolds Manuscripta Math. 94 1997 95-110
15. Jones G.A. Singerman D. Complex Functions. An Algebraic and Geometric Viewpoint 1987 Cambridge University Press Cambridge
16. Kanai M. Rough isometries and combinatorial approximations of geometries of non-compact Riemannian manifolds J. Math. Soc. Japan 37 1985 391-413
17. Kanai M. Rough isometries and the parabolicity of Riemannian manifolds J. Math. Soc. Japan 38 1986 227-238
18. Kanai M. Analytic inequalities and rough isometries between non-compact Riemannian manifolds in: Curvature and Topology of Riemannian Manifolds, Katata, 1985 in: Lecture Notes in Math. vol. 1201 1986 122-137 Springer Berlin
19. Paulin F. On the critical exponent of a discrete group of hyperbolic isometries Differential Geom. Appl. 7 1997 231-236
20. A. Portilla, J.M. Rodríguez, E. Tourís, Gromov hyperbolicity through decomposition of metric spaces II, J. Geom. Anal., submitted for publication
21. Randol B. Cylinders in Riemann surfaces Comment. Math. Helv. 54 1979 1-5
22. Rodríguez J.M. Isoperimetric inequalities and Dirichlet functions of Riemann surfaces Publ. Mat. 38 1994 243-253
23. Rodríguez J.M. Two remarks on Riemann surfaces Publ. Mat. 38 1994 463-477
24. Rodríguez J.M. Tourís E. Gromov hyperbolicity through decomposition of metric spaces Acta Math. Hung. 103 2004 53-84
25. J.M. Rodríguez, E. Tourís, Simple closed geodesics determine the Gromov hyperbolicity of Riemann surfaces, Preprint
26. J.M. Rodríguez, E. Tourís, Gromov hyperbolicity of Riemann surfaces, Preprint
27. Shimizu H. On discontinuous groups operating on the product of upper half-planes Ann. of Math. 77 1963 33-71
28. Soardi P.M. Rough isometries and Dirichlet finite harmonic functions on graphs Proc. Amer. Math. Soc. 119 1993 1239-1248
29. Sullivan D. Related aspects of positivity in Riemannian Geometry J. Diff. Geom. 25 1987 327-351