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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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Brownian motion and a generalised little Picard’s theorem
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by Wilfrid S. Kendall PDF
Trans. Amer. Math. Soc. 275 (1983), 751-760 Request permission

Abstract:

Goldberg, Ishihara, and Petridis have proved a generalised little Picard’s theorem for harmonic maps; if a harmonic map of bounded dilatation maps euclidean space, for example, into a space of negative sectional curvatures bounded away from zero then that map is constant. In this paper a probabilistic proof is given of a variation on this result, requiring in addition that the image space has curvatures bounded below. The method involves comparing asymptotic properties of Brownian motion with the asymptotic behaviour of its image under such a map.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 275 (1983), 751-760
  • MSC: Primary 58G32; Secondary 32H30, 53C20
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0682729-8
  • MathSciNet review: 682729