[Liouville property and the linear drift of Brownian motion]
Let M be a complete connected Riemannian manifold with bounded sectional curvature. Under the assumption that M is a regular covering of a manifold with finite volume, we establish that M is Liouville if, and only if, the linear rate of escape of Brownian motion on M vanishes.
Soit M une variété riemannienne complète connexe de courbure sectionnelle bornée. Si M est le revêtement régulier d'une variété de volume fini, alors il n'y a pas de fonctions harmoniques bornées non constantes si, et seulement si, la vitesse de fuite du mouvement brownien est nulle.
Accepted:
Published online:
Anders Karlsson 1; François Ledrappier 2
@article{CRMATH_2007__344_11_685_0, author = {Anders Karlsson and Fran\c{c}ois Ledrappier}, title = {Propri\'et\'e de {Liouville} et vitesse de fuite du mouvement brownien}, journal = {Comptes Rendus. Math\'ematique}, pages = {685--690}, publisher = {Elsevier}, volume = {344}, number = {11}, year = {2007}, doi = {10.1016/j.crma.2007.04.019}, language = {fr}, }
Anders Karlsson; François Ledrappier. Propriété de Liouville et vitesse de fuite du mouvement brownien. Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 685-690. doi : 10.1016/j.crma.2007.04.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.04.019/
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