5 problems

Let $p\ge 2$ and let $\phi:U\to\mathbb{C}$ be a complex-valued $(p,1)$-harmonic morphism defined locally on the standard Euclidean space $\mathbb{R}^{2p-1}$. The nonexistence conje…

Existence conjecture. There exists a complex-valued harmonic morphism

Let $(M^m,g)$ be an irreducible Riemannian symmetric space of dimension $m\ge 2$. For each point $p\in M$, a complex valued harmonic morphism is a harmonic morphism … defined on an…

Gudmundsson's conjecture. For each point $p\in M$, there exists a complex-valued harmonic morphism

Let $(M^m,g)$ be an irreducible Riemannian symmetric space of dimension $m\ge 2$. For each point $p\in M$, consider complex-valued harmonic morphisms defined on an open neighbourho…