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.
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.
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@article{CRMATH_2007__344_11_685_0,
author = {Karlsson, Anders and Ledrappier, Fran\c{c}ois},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.04.019/}
}
TY - JOUR AU - Karlsson, Anders AU - Ledrappier, François TI - Propriété de Liouville et vitesse de fuite du mouvement brownien JO - Comptes Rendus. Mathématique PY - 2007 SP - 685 EP - 690 VL - 344 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.04.019/ DO - 10.1016/j.crma.2007.04.019 LA - fr ID - CRMATH_2007__344_11_685_0 ER -
%0 Journal Article %A Karlsson, Anders %A Ledrappier, François %T Propriété de Liouville et vitesse de fuite du mouvement brownien %J Comptes Rendus. Mathématique %D 2007 %P 685-690 %V 344 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2007.04.019/ %R 10.1016/j.crma.2007.04.019 %G fr %F CRMATH_2007__344_11_685_0
Karlsson, Anders; Ledrappier, François. Propriété de Liouville et vitesse de fuite du mouvement brownien. Comptes Rendus. Mathématique, Tome 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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