4 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 March's criterion for transience on rotationally symmetric manifolds
Jhon E. Bravo, Jean C. Cortissoz
In this short paper we show that March's criterion for the existence of a bounded non constant harmonic function on a weak model is also a necessary and sufficient condition for th…