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Revista Matemática Iberoamericana


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Volume 23, Issue 1, 2007, pp. 1–16
DOI: 10.4171/RMI/484

Published online: 2007-04-30

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

Frédéric Mouton[1]

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

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

Keywords: Harmonic functions, Fatou type theorems, area integral, negative curvature, Brownian motion

Mouton Frédéric: Local Fatou theorem and the density of energy on manifolds of negative curvature. Rev. Mat. Iberoam. 23 (2007), 1-16. doi: 10.4171/RMI/484