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Stochastic Integrals pp 479–491Cite as

Brownian motion, negative curvature, and harmonic maps

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 851))

Abstract

As mentioned above, it has been the purpose of this article to show that Brownian motion and probabilistic techniques can be applied to prove results in geometric function theory. The main result obtained, at 4.2, is weaker than the corresponding result at 3.1 proved by geometric methods. However it is possible to extend 4.2, for example by relaxing the curvature conditions to hold only off a compact set.

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7. References

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Authors and Affiliations

  1. Department of Mathematical Statistics, The University, Hull

    W. S. Kendall

Authors
  1. W. S. Kendall
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David Williams

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© 1981 Springer-Verlag

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Kendall, W.S. (1981). Brownian motion, negative curvature, and harmonic maps. In: Williams, D. (eds) Stochastic Integrals. Lecture Notes in Mathematics, vol 851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088739

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  • DOI: https://doi.org/10.1007/BFb0088739

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10690-6

  • Online ISBN: 978-3-540-38613-1

  • eBook Packages: Springer Book Archive

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