论文标题
$ p $ - 谐波且复杂的等式式函数$ \ mathbb {r}^m \ ltimes \ mathbb {r}^n $和$ \ mathbb {r}^m \ ltimes \ ltimes \ ltimes \ mathrm {h}
$p$-Harmonic and Complex Isoparametric Functions on the Lie Groups $\mathbb{R}^m \ltimes \mathbb{R}^n$ and $\mathbb{R}^m \ltimes \mathrm{H}^{2n+1}$
论文作者
论文摘要
在本文中，我们介绍了关于Riemannian歧管上复杂的等摄影功能的新概念。然后使用这些来设计一种构建适当的$ p $ harmonic功能的通用方法。然后，我们将其应用于Lie Group semidirect产品上的首个已知的明确$ p $ -Harmonic函数$ \ MATHBB {r}^M \ ltimes \ Mathbb {r}^n $和$ \ Mathbb {r} $ \ mathrm {h}^{2n+1} $表示经典$（2N+1）$ - 维度heisenberg group。特别是，我们在所有简单连接的不可还原的四维谎言组上构建了此类示例。
In this paper we introduce the new notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper $p$-harmonic functions. We then apply this to construct the first known explicit proper $p$-harmonic functions on the Lie group semidirect products $\mathbb{R}^m \ltimes \mathbb{R}^n$ and $\mathbb{R}^m \ltimes \mathrm{H}^{2n+1}$, where $\mathrm{H}^{2n+1}$ denotes the classical $(2n+1)$-dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.
