The nonsolvability of the Dirichlet problem on negatively curved manifolds

DOI10.1016/S0926-2245(98)00008-4zbMath0947.53019WikidataQ115337509 ScholiaQ115337509MaRDI QIDQ1295455

Albert Borbe'ly

Publication date: 12 November 2000

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

zbMATH Keywords

Dirichlet problemharmonic functionconvex setnegatively curved manifold

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 (10)

Asymptotic Dirichlet problem for the $p$-Laplacian on Cartan-Hadamard manifolds ⋮ Existence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature ⋮ Martin compactification of a complete surface with negative curvature ⋮ On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold ⋮ Convexity at infinity in Cartan-Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems ⋮ Some results on the convex hull of finitely many convex sets ⋮ Dirichlet problem at infinity on Gromov hyperbolic metric measure spaces ⋮ Solvability of minimal graph equation under pointwise pinching condition for sectional curvatures ⋮ Survey on the asymptotic Dirichlet problem for the minimal surface equation ⋮ Regularity at infinity of Hadamard manifolds with respect to some elliptic operators and applications to asymptotic Dirichlet problems

Cites Work

• The Dirichlet problem at infinity for manifolds of negative curvature
• The Dirichlet problem at infinity for a negatively curved manifold
• Positive harmonic functions on complete manifolds of negative curvature
• Negatively curved manifolds, elliptic operators, and the Martin boundary
• Convexity at infinity and Brownian motion on manifolds with unbounded negative curvature
• Visibility manifolds
• Asymptotic Dirichlet Problems for Harmonic Functions on Riemannian Manifolds
• Brownian Motion and Harmonic Functions on Manifolds of Negative Curvature
• Construction of Convex Sets in Negatively Curved Manifolds
• The limiting angle of certain riemannian brownian motions
• On a characterization of flow‐invariant sets

This page was built for publication: The nonsolvability of the Dirichlet problem on negatively curved manifolds