Hausdorff Dimension of Harmonic Measures on Negatively Curved Manifolds

DOI10.2307/2001325zbMath0702.58080OpenAlexW4237316840WikidataQ125658216 ScholiaQ125658216MaRDI QIDQ3480975

François Ledrappier, Yuri Kifer

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2001325

zbMATH Keywords

Hausdorff dimensionharmonic measurestochastic analysis

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Global Riemannian geometry, including pinching (53C20) Potential theory on Riemannian manifolds and other spaces (31C12)

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Unnamed Item, Central limit theorem of Brownian motions in pinched negative curvature, Ergodic theory on Galton—Watson trees: speed of random walk and dimension of harmonic measure, Theorie du Potentiel sur les Graphes et les Varietes, Conditional measure and flip invariance of Bowen-Margulis and harmonic measures on manifolds of negative curvature, Harmonic quasi-isometric maps. III: Quotients of Hadamard manifolds, Large deviations for random walks on Gromov-hyperbolic spaces, Harmonic measures on negatively curved manifolds, The ergodic theory of discrete isometry groups on manifolds of variable negative curvature, Harmonic Measures on Covers of Compact Surfaces of Nonpositive Curvature, Dimension of harmonic measures in hyperbolic spaces, Harmonic quasi-isometric maps. II: Negatively curved manifolds, The Poisson boundary of covering Markov operators, Spectrum, harmonic functions, and hyperbolic metric spaces, Harmonic functions on ℝ-covered foliations, The Hausdorff dimension of the harmonic class on negatively curved surfaces, Ergodic properties of Brownian motion on covers of compact negatively-curve manifolds, Dimensional properties of the harmonic measure for a random walk on a hyperbolic group, A lower bound for Hausdorff dimensions of harmonic measures on negatively curved manifolds

Cites Work

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• On the Harnack inequality for linear elliptic equations
• Positive harmonic functions on complete manifolds of negative curvature
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• The ergodic theory of axiom A flows
• Smoothness of horocycle foliations
• Dimension, entropy and Lyapunov exponents
• Four applications of conformal equivalence to geometry and dynamics
• On Harnack's theorem for elliptic differential equations
• Ergodic properties of Brownian motion on covers of compact negatively-curve manifolds
• Symbolic Dynamics for Hyperbolic Flows
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms