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April, 2007 Local Fatou theorem and the density of energy on manifolds of negative curvature
Frédéric Mouton
Rev. Mat. Iberoamericana 23(1): 1-16 (April, 2007).

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.

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Frédéric Mouton . "Local Fatou theorem and the density of energy on manifolds of negative curvature." Rev. Mat. Iberoamericana 23 (1) 1 - 16, April, 2007.

Information

Published: April, 2007
First available in Project Euclid: 1 June 2007

zbMATH: 1131.31004
MathSciNet: MR2351124

Subjects:
Primary: 31C12, 31C35, 58J65, 60J45

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.23 • No. 1 • April, 2007
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