Revista Matemática Iberoamericana
- Rev. Mat. Iberoamericana
- Volume 23, Number 1 (2007), 1-16.
Local Fatou theorem and the density of energy on manifolds of negative curvature
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.
Rev. Mat. Iberoamericana, Volume 23, Number 1 (2007), 1-16.
First available in Project Euclid: 1 June 2007
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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