### On the Hausdorff dimension of harmonic measure in higher dimension.

J. Bourgain (1987)

Inventiones mathematicae

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J. Bourgain (1987)

Inventiones mathematicae

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Kurki, Jukka (1995)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

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Premalatha, T. Sowmya (2000)

Annales mathématiques Blaise Pascal

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Eiderman, Vladimir, Essén, Matts (1996)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

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J. Bourgain, T. Wolff (1990)

Colloquium Mathematicae

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I. Popovici, Alexander Volberg (1996)

Fundamenta Mathematicae

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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...

Ursula Hamenstädt (1990)

Mathematische Zeitschrift

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Giuseppe Devillanova, Sergio Solimini (2007)

Rendiconti del Seminario Matematico della Università di Padova

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James A. Jenkins (1973/74)

Mathematische Zeitschrift

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Marcello Lucia, Michael J. Puls (2015)

Analysis and Geometry in Metric Spaces

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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.