The Oshima-Sekiguchi and Liouville theorems on Heintze groups

DOI10.1016/j.jfa.2005.12.002zbMath1106.58011OpenAlexW2031645795MaRDI QIDQ2497906

Richard C. Penney

Publication date: 4 August 2006

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2005.12.002

zbMATH Keywords

Liouville theoremasymptotic expansionshomogeneous spacePoisson kernelelliptic operatorsolvable Lie groupsnegatively curved Riemannian manifoldOshima-Sekiguchi theorem

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05)

Cites Work

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• The Dirichlet problem at infinity for manifolds of negative curvature
• The Dirichlet problem at infinity for a negatively curved manifold
• Negatively curved manifolds, elliptic operators, and the Martin boundary
• Eigenspaces of invariant differential operators on an affine symmetric space
• Harmonic functions on manifolds
• Harmonic sections of polynomial growth
• van den Ban-Schlichtkrull-Wallach asymptotic expansions on nonsymmetric domains
• On homogeneous manifolds of negative curvature
• Unbounded harmonic functions on homogeneous manifolds of negative curvature
• A smooth subadditive homogeneous norm on a homogeneous group
• Boundaries for left-invariant sub-elliptic operators on semidirect products of nilpotent and abelian groups.
• Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups
• Homogeneous Manifolds with Negative Curvature. I
• Homogeneous manifolds with negative curvature. II
• Cauchy problems with characteristic initial hypersurface

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