Completeness and existence of bounded biharmonic functions on a Riemannian manifold

DOI10.5802/aif.502zbMath0273.31010OpenAlexW2327284817WikidataQ115158997 ScholiaQ115158997MaRDI QIDQ2264890

Leo Sario

Publication date: 1974

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1974__24_1_311_0

Mathematics Subject Classification ID

Biharmonic and polyharmonic equations and functions in higher dimensions (31B30)

Related Items (3)

Bounded biharmonic functions on the Poincaré $N$-ball ⋮ A relation between biharmonic Green’s functions of simply supported and clamped bodies ⋮ Harmonic and quasiharmonic degeneracy of Riemannian manifolds

Cites Work

• Classification theory of Riemannian manifolds. Harmonic, quasiharmonic and biharmonic functions
• Negative quasiharmonic functions
• Bounded polyharmonic functions and the dimension of the manifold
• Behavior of biharmonic functions on Wiener's and Royden's compactifications
• Generators of the space of bounded biharmonic functions
• Polyharmonic classification of Riemannian manifolds
• The class of \((p,q)\)-biharmonic functions
• Existence of Dirichlet finite biharmonic functions on the Poincaré 3-ball
• Parabolicity and existence of bounded biharmonic functions
• Counterexamples in the biharmonic classification of Riemannian 2-manifolds
• Radial quasiharmonic functions
• Dirichlet finite biharmonic functions with Dirichlet finite Laplacians
• Dirichlet finite biharmonic functions on the plane with distorted metrics
• Dirichlet finite biharmonic functions on the Poincaré N-ball.
• Riemannian Manifolds of Dimension N ⩾ 4 without Bounded Biharmonic Functions
• Parabolicity and Existence of Dirichlet Finite Biharmonic Functions
• Harmonic and biharmonic degeneracy
• COMPLETENESS AND FUNCTION-THEORETIC DEGENERACY OF RIEMANNIAN SPACES
• Quasiharmonic Classification of Riemannian Manifolds
• A Property of Biharmonic Functions with Dirichlet Finite Laplacians.
• Positive harmonic functions and biharmonic degeneracy
• Biharmonic classification of Riemannian manifolds
• N-manifolds carrying bounded but no Dirichlet finite harmonic functions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Completeness and existence of bounded biharmonic functions on a Riemannian manifold