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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Hausdorff dimension of harmonic measures on negatively curved manifolds


Authors: Yuri Kifer and François Ledrappier
Journal: Trans. Amer. Math. Soc. 318 (1990), 685-704
MSC: Primary 58G32; Secondary 60J60
DOI: https://doi.org/10.1090/S0002-9947-1990-0951889-7
MathSciNet review: 951889
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Abstract: We show by probabilistic means that harmonic measures on manifolds, whose curvature is sandwiched between two negative constants have positive Hausdorff dimensions. A lower bound for harmonic measures of open sets is derived, as well. We end with the results concerning the Hausdorff dimension of harmonic measures on universal covers of compact negatively curved manifolds.


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DOI: https://doi.org/10.1090/S0002-9947-1990-0951889-7
Article copyright: © Copyright 1990 American Mathematical Society