A discrete analogue of the harmonic morphism and green kernel comparison theorems
A discrete analogue of the harmonic morphism and green kernel comparison theorems
复制标题
调和态射和绿核比较定理的离散模拟
DOI：
10.1017/s0017089500030019
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发表时间：
2000
影响因子：
0.5
通讯作者：
H. Urakawa
中科院分区：
文献类型：
--
作者：
H. Urakawa
我们给出两个黎曼流形之间的调和态射的离散模拟。粗略地说，这是两个保留局部调和函数的图之间的映射。我们用水平共形来表征调和态射。给出了许多例子，包括覆盖、非完全扩展 p-sum 和折叠。引入水平和垂直拉普拉斯算子，获得调和态射的格林核估计。作为应用，获得了无限树的格林核的一般且敏锐的估计。
We give a discrete analogue of the harmonic morphism between two Riemannian manifolds. Roughly speaking, this is a mapping between two graphs preserving local harmonic functions. We characterize harmonic morphisms in terms of horizontal conformality. Many examples including coverings, non-complete extended p-sums and collapsings are given. Introducing the horizontal and vertical Laplacians, the Green kernel estimates are obtained for the harmonic morphism. As applications, a general and sharp estimate of the Green kernel for an infinite tree is obtained.