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

TL;DR

This paper extends Milnor's classical result, which characterizes the nature of rotationally symmetric surfaces as parabolic or hyperbolic, to the broader context of biharmonic functions, providing new insights into surface classification.

Contribution

The paper generalizes Milnor's criterion from harmonic to biharmonic functions, offering a novel method to classify surfaces based on biharmonicity.

Findings

Extended Milnor's criterion to biharmonic functions

Provided new classification tools for surfaces

Enhanced understanding of surface geometry in biharmonic context

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.