The p-harmonic boundary for quasi-isometric graphs and manifolds

2010/02/04 by Puls, Michael J.
#31C12 #31C20 #43A15 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1002.1061

Abstract

Let p be a real number greater number greater than one. Suppose that a graph G of bounded degree is quasi-isometric with a Riemannian manifold M with certain properties. Under these conditions we will show that the p-harmonic boundary of G is homeomorphic to the p-harmonic boundary of M. We will also prove that there is a bijection between the p-harmonic functions on G and the p-harmonic functions on M.

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