On Milnor's criterion for deciding whether a surface is hyperbolic or parabolic for biharmonic functions

2025/02/07 by Bravo, John E., Cortissoz, Jean C. · 2 citations
#31C05 #53C21 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.05249

Abstract

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.

Cited by

• A Polyharmonic Liouville Hierarchy on Complete Manifolds of Nonnegative Ricci Curvature
• Liouville theorem for biharmonic functions on manifolds of nonnegative Ricci curvature

Related

• Biharmonic surfaces of \mathbbS⁴
• Biharmonic hypersurfaces in a product space L^m× ℝ
• Remarks on biharmonic hypersurfaces in space forms
• Linear Weingarten surfaces in Euclidean and hyperbolic space
• Parabolic Weingarten surfaces in hyperbolic space