ENERGY FINITE p-HARMONIC FUNCTIONS ON GRAPHS AND ROUGH ISOMETRIES

Title & Authors
ENERGY FINITE p-HARMONIC FUNCTIONS ON GRAPHS AND ROUGH ISOMETRIES
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 $\small{\mathbf{R}^l}$, where $\small{l}$ is the number of p-hyperbolic ends of G. Furthermore, we prove that if a graph G is roughly isometric to G, then $\small{\mathcal{HBD}_p(G)}$ is also in an one to one correspondence with $\small{\mathbf{R}^l}$.
Keywords
p-harmonic function;almost every path;rough isometry;
Language
English
Cited by
1.
Graphs of bounded degree and thep-harmonic boundary, Pacific Journal of Mathematics, 2010, 248, 2, 429
2.
THE -HARMONIC BOUNDARY AND -MASSIVE SUBSETS OF A GRAPH OF BOUNDED DEGREE, Bulletin of the Australian Mathematical Society, 2014, 89, 01, 149
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