Biharmonic functions on spheres and hyperbolic spaces

TL;DR

This paper constructs explicit proper r-harmonic functions on spheres and hyperbolic spaces, expanding the class of known solutions in differential geometry.

Contribution

It introduces new explicit proper r-harmonic functions on spheres and hyperbolic spaces for all r ≥ 1 and n ≥ 2, which were not previously known.

Findings

Explicit proper r-harmonic functions constructed for spheres and hyperbolic spaces.

Applicable for all r ≥ 1 and dimensions n ≥ 2.

Enhances understanding of harmonic analysis on curved spaces.

Abstract

We construct new explicit proper r-harmonic functions on the standard n-dimensional sphere S^n and hyperbolic space H^n for any r\ge 1 and n\ge 2.