5 papers · 1 filter
A Polyharmonic Liouville Hierarchy on Complete Manifolds of Nonnegative Ricci Curvature
John E. Bravo, Jean C. Cortissoz
In this paper, we establish a complete Liouville--type hierarchy for polyharmonic functions on Riemannian manifolds with nonnegative Ricci curvature. Extending Yau's classical resu…
Liouville theorem for biharmonic functions on manifolds of nonnegative Ricci curvature
John E. Bravo, Jean C. Cortissoz
In this paper we extend Yau's celebrated Liouville theorem to the biharmonic case. Namely, we show that in a complete Riemannian manifold with a pole and nonnegative Ricci curvatur…
On Milnor's criterion for deciding whether a surface is hyperbolic or parabolic for biharmonic functions
John E. Bravo, Jean C. Cortissoz
In this paper we generalise a celebrated result of Milnor that characterises whether a rotationally symmetric surface is parabolic or hyperbolic to the case of biharmonic functions…
On the Dirichlet problem at infinity on three-manifolds of negative curvature
Jean C. Cortissoz, Ramón Urquijo Novella
In this paper we prove that in a three-manifold with finitely many expansive ends, such that each end has a neighborhood where the curvature is bounded above by a negative constant…
On the behaviour of harmonic functions on Riemannian cones
Jean C. Cortissoz
We discuss the behavior of harmonic functions on Riemannian cones as defined below and Lioville's theorem.