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

DOI10.4171/RMI/484zbMath1131.31004MaRDI QIDQ997806

Frédéric Mouton

Publication date: 7 August 2007

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/43581

zbMATH Keywords

Brownian motionFatou type theoremsharmonic functionsnegative curvature

Mathematics Subject Classification ID

Martin boundary theory (31C35) Probabilistic potential theory (60J45) Diffusion processes and stochastic analysis on manifolds (58J65) Potential theory on Riemannian manifolds and other spaces (31C12)

Cites Work

• On the existence of boundary values for harmonic functions in several variables
• The density of the area integral in \({\mathbb{R}}_+^{n+1}\)
• Positive harmonic functions on complete manifolds of negative curvature
• Negatively curved manifolds, elliptic operators, and the Martin boundary
• Densité de l'intégrale d'aire dans \({\mathbb{R}}_+^{n+1}\) et limites non tangentielles. (Density of the area integral in \({\mathbb{R}}_ +^{n+1}\) and non-tangential limits)
• Boundary behavior of functions on complete manifolds of negative curvature
• Asymptotic behaviour of harmonic functions in negative curvature
• Conditional brownian motion and the boundary limits of harmonic functions
• Differential equations on riemannian manifolds and their geometric applications
• Local Fatou Theorem and Area Theorem for Symmetric Spaces of Rank One
• Admissible convergence in Cartan-Hadamard manifolds.
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