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November, 1983 Brownian Motion, Geometry, and Generalizations of Picard's Little Theorem
S. I. Goldberg, C. Mueller
Ann. Probab. 11(4): 833-846 (November, 1983). DOI: 10.1214/aop/1176993435


Brownian motion is introduced as a tool in Riemannian geometry to show how useful it is in the function theory of manifolds, as well as the study of maps between manifolds. As applications, a generalization of Picard's little theorem, and a version of it for Riemann surfaces of large genus are given.


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S. I. Goldberg. C. Mueller. "Brownian Motion, Geometry, and Generalizations of Picard's Little Theorem." Ann. Probab. 11 (4) 833 - 846, November, 1983.


Published: November, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0523.60073
MathSciNet: MR714949
Digital Object Identifier: 10.1214/aop/1176993435

Primary: 32H25
Secondary: 53C21 , 60J65

Keywords: Brownian motion , harmonic and quasiconformal mappings , sectional curvature , tail $\sigma$-field

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 4 • November, 1983
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