논문KCI 등재
Energy finite $p$-harmonic functions on graphs and rough isometries
대한수학회 (The Korean Mathematical Society)|2007.04|대한수학회논문집 (Communications of the KMS)|제22권 제2호|pp. 277-287
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Abstract
We prove that if a graph G of bounded degree has finitely many p-hyperbolic ends (1<p<infty)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 Gis in one to one corresponding to 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 {bf R}^l.
참고문헌 (9)
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관련 논문AI추천
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