Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2007.04.30
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Abstract

We prove that if a graph G of bounded degree has finitely many p-hyperbolic ends($1) in which every bounded energy finite p-harmonic function is asymptotically constant for almost every path, then the set $\mathcal{HBD}_p(G)$ 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 $\mathbf{R}^l$.

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References

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Cited by

  1. Graphs of bounded degree and thep-harmonic boundary vol.248, pp.2, 2010, https://doi.org/10.2140/pjm.2010.248.429
  2. THE -HARMONIC BOUNDARY AND -MASSIVE SUBSETS OF A GRAPH OF BOUNDED DEGREE vol.89, pp.01, 2014, https://doi.org/10.1017/S0004972713000439