Generalized harmonic functions of Riemannian manifolds with ends

DOI10.1007/S00209-011-0943-2zbMath1259.53062OpenAlexW2086998136WikidataQ115388781 ScholiaQ115388781MaRDI QIDQ455624

S. A. Korol'kov, Alexander G. Losev

Publication date: 22 October 2012

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-011-0943-2

zbMATH Keywords

Liouville theoremboundary problem for L-harmonic functionsHarnack type inequalityL-harmonic functionnon-parabolic end

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (12)

Liouville type theorems for solutions of semilinear equations on non-compact Riemannian manifolds ⋮ Asymptotic behavior of solutions of the Dirichlet problem for the Poisson equation on model Riemannian manifolds ⋮ Classification of metric measure spaces and their ends using p-harmonic functions ⋮ On the existence of solutions of the Dirichlet problem for the \(p\)-Laplacian on Riemannian manifolds ⋮ On the existence of solutions of the Neumann problem for the \(p \)-Laplacian on parabolic manifolds with a model end ⋮ On the solvability of boundary value problems for the stationary Schrödinger equation in unbounded domains on Riemannian manifolds ⋮ On capacitary characteristics of noncompact Riemannian manifolds ⋮ Dimensions of solution spaces of the Schrödinger equation with finite Dirichlet integral on non-compact Riemannian manifolds ⋮ Existence of solutions to the second boundary-value problem for the \(p\)-Laplacian on Riemannian manifolds ⋮ On solvability of the boundary value problems for harmonic function on noncompact Riemannian manifolds ⋮ A note on some remarkable differential equations on a Riemannian manifold ⋮ On the existence of solutions of the Neumann problem for the \(p \)-Laplacian on hyperbolic manifolds with a model end

Cites Work

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• Positive harmonic functions on complete manifolds of negative curvature
• Harmonic functions and the structure of complete manifolds
• Unbounded solutions of the stationary Schrödinger equation on Riemannian manifolds
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Generalized Liouville property for Schrödinger operator on Riemannian manifolds

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