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arXiv · 2007.14819

Explicit harmonic morphisms and $p$-harmonic functions from the complex and quaternionic Grassmannians

Elsa Ghandour·Sigmundur Gudmundsson
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Abstract

We construct explicit complex-valued $p$-harmonic functions and harmonic morphisms on the classical compact symmetric complex and quaternionic Grassmannians. The ingredients for our construction method are joint eigenfunctions of the classical Laplace-Beltrami and the so called conformality operator. A known duality principle implies that these $p$-harmonic functions and harmonic morphisms also induce such solutions on the Riemannian symmetric non-compact dual spaces.

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Elsa Ghandour, Sigmundur Gudmundsson. 2023-08-20. Explicit harmonic morphisms and $p$-harmonic functions from the complex and quaternionic Grassmannians. https://arxiv.org/abs/2007.14819

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