Fisher information geometry, Poisson kernel and asymptotical harmonicity

DOI10.1016/J.DIFGEO.2011.04.015zbMath1227.53050OpenAlexW2042522067WikidataQ115356901 ScholiaQ115356901MaRDI QIDQ719827

Mitsuhiro Itoh, Hiroyasu Satoh

Publication date: 12 October 2011

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2011.04.015

zbMATH Keywords

Busemann functionPoisson kernelvisibilityHadamard manifoldFisher information metricasymptotically harmonic

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Global Riemannian geometry, including pinching (53C20) Statistical aspects of information-theoretic topics (62B10)

Related Items (4)

Harmonic functions on rank one asymptotically harmonic manifolds ⋮ Information geometry of Busemann-barycenter for probability measures ⋮ Information geometry of the space of probability measures and barycenter maps ⋮ Horospheres and hyperbolicity of Hadamard manifolds

Cites Work

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• Homogeneous Riemannian manifolds and the visibility axiom
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• Manifolds of nonpositive curvature
• Geometry of horospheres
• The Lichnerowicz conjecture on harmonic manifolds
• Generalized Heisenberg groups and Damek-Ricci harmonic spaces
• Einstein metrics with nonpositive sectional curvature on extensions of Lie algebras of Heisenberg type
• Riemannian geometry and geometric analysis.
• Entropy and rigidity of locally symmetric spaces of strictly negative curvature
• Geometry of harmonic maps
• On Riemannian manifolds admitting a function whose gradient is of constant norm
• On harmonic and asymptotically harmonic homogeneous spaces
• Visibility manifolds
• HOROSPHERES AND HYPERBOLIC SPACES
• A Poisson kernel on Heisenberg type nilpotent groups
• A class of nonsymmetric harmonic Riemannian spaces
• Die Fisher-Information und symplektische Strukturen
• Some results in E. Cartan's theory of isoparametric families of hypersurfaces
• Compactifications of symmetric spaces

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