Brownian Motion, Geometry, and Generalizations of Picard's Little Theorem
Open Access
- 1 November 1983
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 11 (4) , 833-846
- https://doi.org/10.1214/aop/1176993435
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.Keywords
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