Harmonic functions of general graph Laplacians
Harmonic functions of general graph Laplacians
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DOI：
10.1007/s00526-013-0677-6
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发表时间：
2013-10
影响因子：
2.1
通讯作者：
B. Hua;M. Keller
中科院分区：
文献类型：
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作者：
B. Hua;M. Keller
我们研究一般加权图上的调和函数，它允许相容的内在度量。我们证明了一个Liouville型定理，它是调和函数的一个定量积分估计，类似于黎曼流形上的Karp定理。作为推论，我们得到了图的Yau's-Liouville型定理，确定了半群的生成元的定义域，并得到了常返性的一个判别准则。作为副积，我们给出了一个类似于Yau'sCaccioppoli不等式的结果.此外，我们还得到了图上调和函数和从图到Hadamard空间的调和映射的各种Liouville型结果。
We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove anLiouville type theorem which is a quantitative integralestimate of harmonic functions analogous to Karp’s theorem for Riemannian manifolds. As corollaries we obtain Yau’s-Liouville type theorem on graphs, identify the domain of the generator of the semigroup onand get a criterion for recurrence. As a side product, we show an analogue of Yau’sCaccioppoli inequality. Furthermore, we derive various Liouville type results for harmonic functions on graphs and harmonic maps from graphs into Hadamard spaces.