Harmonic maps are viewed as maps sending a fixed diffusion to
manifold-valued martingales.Under a convexity condition, we prove that the
continuity of real-valued harmonic functions implies the continuity of harmonic
maps. Then we prove with a probabilistic method that continuous harmonic maps
are smooth under Hörmander’s condition; the proof relies on the
study of martingales with values in the tangent bundle.
Publié le : 2000-04-14
Classification:
Harmonic maps,
manifold-valued martingales,
stochastic calculus on manifolds,
Malliavin calculus,
58G32,
58E20,
60G48,
60H07
@article{1019160255,
author = {Picard, Jean},
title = {Smoothness of harmonic maps for hypoelliptic diffusions},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 643-666},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160255}
}
Picard, Jean. Smoothness of harmonic maps for hypoelliptic diffusions. Ann. Probab., Tome 28 (2000) no. 1, pp. 643-666. http://gdmltest.u-ga.fr/item/1019160255/