Generalized harmonic maps and representations of discrete groups
Generalized harmonic maps and representations of discrete groups
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离散群的广义调和图和表示
DOI：
10.4310/cag.2000.v8.n3.a5
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发表时间：
2000
影响因子：
0.7
通讯作者：
Mu
中科院分区：
文献类型：
--
作者：
Mu
本文研究了从单纯复形到（整体）非正曲率完备度量空间的广义调和映射。证明了如果单纯复形有一个满足局部组合条件的“容许权”，则任何这样的广义调和映射必是常数映射。局部组合条件是图的第一特征值的非线性推广。这在阿基米德和非阿基米德的可表示群的表示中有应用。
This paper considers generalized harmonic maps from a simplicial complex to a complete metric space of (globally) non-positive curvature. It is proved that if a simplicial complex admits an "admissible weight" satisfying a local combinatorial condition, then any such generalized harmonic maps must be constant maps. The local combinatorial condition is in terms of a nonlinear generalization of the first eigenvalue of a graph. This has applications in the Archimedean and non-Archimedean representations of finitely presentable groups.