Displaying similar documents to “Harmonic measure of some Cantor type sets.”

Rigidity of harmonic measure

I. Popovici, Alexander Volberg (1996)

Fundamenta Mathematicae


Let J be the Julia set of a conformal dynamics f. Provided that f is polynomial-like we prove that the harmonic measure on J is mutually absolutely continuous with the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. This is no longer true for generalized polynomial-like maps. But for such dynamics the coincidence of classes of these two measures turns out to be equivalent to the existence of a conformal change of variable which reduces the dynamical...

The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces

Marcello Lucia, Michael J. Puls (2015)

Analysis and Geometry in Metric Spaces


Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfies certain conditions. The p-Royden and p-harmonic boundaries of X are constructed by using the p-Royden algebra of functions on X and a Dirichlet type problem is solved for the p-Royden boundary. We also characterize the metric measure spaces whose p-harmonic boundary is empty.