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.
Publié le : 1983-11-14
Classification:
Brownian motion,
harmonic and quasiconformal mappings,
sectional curvature,
tail $\sigma$-field,
32H25,
53C21,
60J65
@article{1176993435,
author = {Goldberg, S. I. and Mueller, C.},
title = {Brownian Motion, Geometry, and Generalizations of Picard's Little Theorem},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 833-846},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993435}
}
Goldberg, S. I.; Mueller, C. Brownian Motion, Geometry, and Generalizations of Picard's Little Theorem. Ann. Probab., Tome 11 (1983) no. 4, pp. 833-846. http://gdmltest.u-ga.fr/item/1176993435/