Explicit $p$-harmonic functions on the real Grassmannians

TL;DR

This paper constructs explicit proper p-harmonic functions on real Grassmannians and flag manifolds using eigenfamilies, revealing new examples of such functions that do not descend from Grassmannians.

Contribution

It introduces a method to explicitly construct proper p-harmonic functions on real Grassmannians and flag manifolds, expanding the known examples in differential geometry.

Findings

Explicit p-harmonic functions on Grassmannians and flag manifolds

Identification of p-harmonic functions not descending from Grassmannians

Application of eigenfamilies method to construct solutions

Abstract

In this work we use the method of eigenfamilies to construct explicit complex-valued proper $p$-harmonic functions on the compact real Grassmannians. We also find proper $p$-harmonic functions on the real flag manifolds which do not descend onto any of the real Grassmannians.