Rough isometry and Dirichlet finite harmonic functions on Riemannian manifolds

Manuscripta Mathematica

Volumn 99, Issue 3, 1999, Pages 311-328

  Lee, Yong Hah ^a  

^a Seoul National University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033161734     PISSN: 00252611     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002290050175     Document Type: Article

References (17)

1. Buser, P.: A note on the isoperimetric constant. Ann. Sci. Éc. Norm. Sup. Paris 15, 213-230 (1982)
2. Croke, C.B.: Some Isoperimetric Inequality and Eigenvalue Estimates. Ann. Sci. Éc. Norm. Sup. 13, 419-435 (1980)
3. Duffin, R.J.: The extremal length of a network. J. Math. Anal. Appl. 5, 200-215 (1962)
4. Glasner M. and Katz, R.: Limits of Dirichlet finite functions along curves. Rocky Mountain J. Math. 12, 429-435 (1982)
5. Grigor'yan, A.A.: The heat equation on noncompact Riemannian manifolds. Mat. Sb. 128 (3), 354-363 (1985); English transl. in Math. USSR-Sb. 56, 349-358 (1987)
6. Grigor'yan, A.A.: The heat equation on noncompact Riemannian manifolds. Mat. Sb. 128 (3), 354-363 (1985); English transl. in Math. USSR-Sb. 56, 349-358 (1987)
7. Holopainen, I.: Rough isometries and p-harmonic functions with finite Dirichlet integral. Rev. Mat. Iberoamericana 10, 143-176 (1994)
8. Holopainen, I. and Soardi, P.M.: p-harmonic functions on graphs and manifolds, manuscripta math. 94, 95-110 (1997)
9. Kanai, M.: Rough isometries, and combinatorial approximations of geometries of non-compact riemannian manifolds. J. Math. Soc. Japan 37 No.3, 391-413 (1985)
10. Kanai, M.: Rough isometries and the parabolicity of riemannian manifolds. J. Math. Soc. Japan 38 No.2, 227-238 (1986)
11. Kayano, T. and Yamasaki, M.: Boundary limits of discrete Dirichlet potentials. Hiroshima Math. J. 14 No.2, 401-406 (1984)
12. Kim, S.W. and Lee, Y.H.: Rough Isometry, Harmonic Functions and Harmonic Maps on Complete Riemannian Manifolds. J. Korean Math. Soc. 36, (1999)
13. Royden, H.L.: Harmonic functions on open Riemann surface. Trans. Amer. Math. Soc. 73, 40-94 (1952)
14. Sario, L. and Nakai, M.: Classification theory of Riemann surfaces. Berlin-Heidelberg-New York: Springer Verlag, 1970
15. Soardi, P.M.: Rough isometries and Dirichlet finite harmonic functions on graphs. Proc. Amer. Math. Soc. 119, 1239-1248 (1993)
16. Yamasaki, M.: Ideal boundary limit of discrete Dirichlet functions. Hiroshima Math. J. 16 No.2, 353-360 (1986)
17. Yau, S.T.: Harmonic functions on complete Riemannian manifolds. Comm. Pure Appl. Math. 28, 201-228 (1975)