# Local Fatou theorem and the density of energy on manifolds of negative curvature

### Frédéric Mouton

Université de Grenoble I, Saint-Martin-d'Hères, France

## Abstract

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

## Cite this article

Frédéric Mouton, Local Fatou theorem and the density of energy on manifolds of negative curvature. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 1–16

DOI 10.4171/RMI/484