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