Tohoku Mathematical Journal

Rough isometry and the asymptotic Dirichlet problem

Hyeong In Choi, Seok Woo Kim, and Yong Hah Lee

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Tohoku Math. J. (2) Volume 50, Number 3 (1998), 333-348.

First available in Project Euclid: 3 May 2007

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Zentralblatt MATH identifier

Primary: 58G20
Secondary: 31C05: Harmonic, subharmonic, superharmonic functions 31C20: Discrete potential theory and numerical methods 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]


Choi, Hyeong In; Kim, Seok Woo; Lee, Yong Hah. Rough isometry and the asymptotic Dirichlet problem. Tohoku Math. J. (2) 50 (1998), no. 3, 333--348. doi:10.2748/tmj/1178224933.

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  • [A] M T. ANDERSON, The Dirichlet problem at infinity for manifolds of negative curvature, J Differential Geom 18 (1983), 701-721
  • [A-S] M T ANDERSON AND R. SCHOEN, Positive harmonic functions on complete manifolds of negativ curvature, Ann of Math 121 (1985), 429-461
  • [B] P BUSER, A note on the isoperimetric constant, Ann Sci EC Norm Sup Paris 15 (1982), 213-230
  • [C] S Y CHENG, The Dirichlet problem at infinity for nonpositively curved manifolds, Comm Ana Geom 1 (1993), 101-112.
  • [Ch] H I CHOI, Asymptotic Dirichlet problems for harmonic functions on Riemannian manifolds, Trans Amer Math Soc 281 (1984), 691-716
  • [C-S] TH. COULHON AND L. SALOFF-COSTE, Vaetes riemanniennes isometriques a infini, Rev Ma Iberoamericana 11 (1995), 687-726
  • [E-O] P EBERLEIN AND B. O'NEILL, Visibility manifolds, Pacific J Math 46 (1973), 45-109
  • [L-W] P Li AND J. WANG, On harmonic rough-isometries, preprin
  • [Kl] M KANAI, Analytic inequalities, and rough isometrics between noncompact Riemannian manifolds, Lecture Notes in Math 1201, Springer-Verlag, Berlin, Heidelberg, New York, 1981, 122-137
  • [K2] M KANAI, Rough isometries, and combinatorial approximations of geometries of non-compac riemannian manifolds, J Math Soc Japan 37 (1985), 391-413
  • [K3] M KANAI, Rough isometries and the parabolicity of Riemannian manifolds, J Math Soc Japa 38 (1986), 227-238 348H I. CHOI, S W KIM AND Y H. LEE
  • [S-Y] R. SCHOEN AND S. T YAU, Lectures on Differential Geometry, International press, Boston, 1994
  • [S] D SULLIVAN, The Dirichlet problem at infinity for a negatively curved manifold, J Differentia Geom 18 (1983), 723-732.