Explicit p-harmonic functions on rank-one Lie groups of Iwasawa type

TL;DR

This paper constructs explicit proper p-harmonic functions on a broad class of rank-one Lie groups of Iwasawa type, encompassing many classical Riemannian manifolds and spaces with special geometric structures.

Contribution

It provides explicit constructions of p-harmonic functions on rank-one Lie groups of Iwasawa type, extending understanding of harmonic analysis on these geometric spaces.

Findings

Explicit p-harmonic functions are constructed on rank-one Lie groups of Iwasawa type.

The class includes classical Riemannian manifolds such as Damek-Ricci spaces.

The methods apply to various geometric structures like Einstein solvmanifolds and Carnot spaces.

Abstract

We construct explicit proper p-harmonic functions on rank-one Lie groups of Iwasawa type. This class of Lie groups includes many classical Riemannian manifolds such as the rank-one symmetric spaces of non-compact type, Damek-Ricci spaces, rank-one Einstein solvmanifolds and Carnot spaces.