Character varieties and harmonic maps to R-trees
Character varieties and harmonic maps to R-trees
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R 树的字符变体和调和映射
DOI：
10.4310/mrl.1998.v5.n4.a9
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发表时间：
1998
影响因子：
1
通讯作者：
Richard A. Wentworth
中科院分区：
文献类型：
--
作者：
Georgios D. Daskalopoulos;S. Dostoglou;Richard A. Wentworth
证明了紧致黎曼流形的基本群的不可约SL 2（C）表示序列所对应的等变调和映射序列的Korevaar-Schoen极限是到R-树的等变调和映射，R-树是极小的，其长度函数与表示序列的Morgan-Shalen极限射影等价.然后，我们研究了存在的谐波映射时，对树的行动固定结束的影响。
We show that the Korevaar-Schoen limit of the sequence of equivariant harmonic maps corresponding to a sequence of irreducible SL2(C) representations of the fundamental group of a compact Riemannian manifold is an equivariant harmonic map to an R-tree which is minimal and whose length function is projectively equivalent to the Morgan-Shalen limit of the sequence of representations. We then examine the implications of the existence of a harmonic map when the action on the tree fixes an end.