Revista Matemática Iberoamericana

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

Frédéric Mouton

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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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 23, Number 1 (2007), 1-16.

Dates
First available in Project Euclid: 1 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1180728883

Mathematical Reviews number (MathSciNet)
MR2351124

Zentralblatt MATH identifier
1131.31004

Subjects
Primary: 31C12: Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14] 31C35: Martin boundary theory [See also 60J50] 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60] 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Keywords
harmonic functions Fatou type theorems area integral negative curvature Brownian motion

Citation

Mouton, Frédéric. Local Fatou theorem and the density of energy on manifolds of negative curvature. Rev. Mat. Iberoamericana 23 (2007), no. 1, 1--16. https://projecteuclid.org/euclid.rmi/1180728883


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References

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