Géométrie/Probabilités
Propriété de Liouville et vitesse de fuite du mouvement brownien
[Liouville property and the linear drift of Brownian motion]
Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 685-690.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.04.019
Karlsson, Anders 1; Ledrappier, François 2

1 Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Suède
2 Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, États-Unis
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Karlsson, Anders; Ledrappier, François. 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. http://www.numdam.org/articles/10.1016/j.crma.2007.04.019/

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