Energy finite p-harmonic functions on graphs and rough isometries

Seok Woo Kim, Yong Hah Lee

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We prove that if a graph G of bounded degree has finitely many p-hyperbolic ends (1 < p < ∞) in which every bounded energy finite p-harmonic function is asymptotically constant for almost every path, then the set HBDp(G) of all bounded energy finite p-harmonic functions on G is in one to one corresponding to Rl, 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 HBDp(G′) is also in an one to one correspondence with Rl.

Original languageEnglish
Pages (from-to)277-287
Number of pages11
JournalCommunications of the Korean Mathematical Society
Issue number2
StatePublished - 2007


  • Almost every path
  • Rough isometry
  • p-harmonic function


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