Let $u$ be a harmonic function on a complete simply connected
manifold $M$ whose sectional curvatures are bounded between two
negative constants. It is proved here a pointwise criterion of
non-tangential convergence for points of the geometric boundary:
the finiteness of the density of energy, which is the geometric
analogue of the density of the area integral in the Euclidean
half-space.
Publié le : 2007-04-14
Classification:
harmonic functions,
Fatou type theorems,
area integral,
negative curvature,
Brownian motion,
31C12,
31C35,
58J65,
60J45
@article{1180728883,
author = {Mouton
,
Fr\'ed\'eric},
title = {Local Fatou theorem and the density of energy on manifolds of negative curvature},
journal = {Rev. Mat. Iberoamericana},
volume = {23},
number = {1},
year = {2007},
pages = { 1-16},
language = {en},
url = {http://dml.mathdoc.fr/item/1180728883}
}
Mouton
,
Frédéric. Local Fatou theorem and the density of energy on manifolds of negative curvature. Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, pp. 1-16. http://gdmltest.u-ga.fr/item/1180728883/