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http://dx.doi.org/10.4134/CKMS.2007.22.2.277

ENERGY FINITE p-HARMONIC FUNCTIONS ON GRAPHS AND ROUGH ISOMETRIES  

Kim, Seok-Woo (DEPARTMENT OF MATHEMATICS EDUCATION KONKUK UNIVERSITY)
Lee, Yong-Hah (DEPARTMENT OF MATHEMATICS EDUCATION EWHA WOMANS UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.22, no.2, 2007 , pp. 277-287 More about this Journal
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 $\mathbf{R}^l$, where $l$ is the number of p-hyperbolic ends of G. Furthermore, we prove that if a graph G' is roughly isometric to G, then $\mathcal{HBD}_p(G is also in an one to one correspondence with $\mathbf{R}^l$.
Keywords
p-harmonic function; almost every path; rough isometry;
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Times Cited By SCOPUS : 1
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