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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Harmonic measures on covers of compact surfaces of nonpositive curvature
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by M. Brin and Y. Kifer PDF
Trans. Amer. Math. Soc. 340 (1993), 373-393 Request permission

Abstract:

Let $M$ be the universal cover of a compact nonflat surface $N$ of nonpositive curvature. We show that on the average the Brownian motion on $M$ behaves similarly to the Brownian motion on negatively curved manifolds. We use this to prove that harmonic measures on the sphere at infinity have positive Hausdorff dimension and if the geodesic flow on $N$ is ergodic then the harmonic and geodesic measure classes at infinity are singular unless the curvature is constant.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 340 (1993), 373-393
  • MSC: Primary 58G32; Secondary 31B15, 53C21, 60J65
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1124163-9
  • MathSciNet review: 1124163