ENERGY FINITE p-HARMONIC FUNCTIONS ON GRAPHS AND ROUGH ISOMETRIES

- Journal title : Communications of the Korean Mathematical Society
- Volume 22, Issue 2, 2007, pp.277-287
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2007.22.2.277

Title & Authors

ENERGY FINITE p-HARMONIC FUNCTIONS ON GRAPHS AND ROUGH ISOMETRIES

Kim, Seok-Woo; Lee, Yong-Hah;

Kim, Seok-Woo; Lee, Yong-Hah;

Abstract

We prove that if a graph G of bounded degree has finitely many p-hyperbolic ends($1

of all bounded energy finite p-harmonic functions on G is in one to one corresponding to , where is the number of p-hyperbolic ends of G. Furthermore, we prove that if a graph G' is roughly isometric to G, then is also in an one to one correspondence with .

Keywords

p-harmonic function;almost every path;rough isometry;

Language

English

Cited by

References

1.

I. Holopainen and P. M. Soardi, p-harmonic functions on graphs and manifolds, manuscripta math. 94 (1997), 95-110

2.

M. Kanai, Rough isometries, and combinatorial approximations of geometries of non-compact riemannian manifolds, J. Math. Soc. Japan 37 (1985), no. 3, 391-413

3.

M. Kanai, Rough isometries and the parabolicity of riemannian manifolds, J. Math. Soc. Japan 38 (1986), no. 2, 227-238

4.

T. Kayano and M. Yamasaki, Boundary limits of discrete Dirichlet potentials, Hiroshima Math. J. 14 (1984), no. 2, 401-406

5.

S. W. Kim and Y. H. Lee, Generalized Liouville property for Schrodinger operator on Riemannian manifolds, Math. Z. 238 (2001), 355-387

6.

Y. H. Lee, Rough isometry and Dirichlet finite harmonic function on Riemannian manifolds, manuscripta math. 99 (1999), 311-328

7.

T. Nakamura and M. Yamasaki, Generalized extremal length of an infinite network, Hiroshima Math. J. 6 (1976), 95-111

8.

P. M. Soardi, Rough isometries and energy finite harmonic functions on graphs, Proc. Amer. Math. Soc. 119 (1993), 1239-1248

9.

M. Yamasaki, Ideal boundary limit of discrete Dirichlet functions, Hiroshima Math. J. 16 (1986) no. 2, 353-360