Teichmueller flow and Weil-Petersson flow
Teichmueller flow and Weil-Petersson flow
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Teichmueller 流和 Weil-Petersson 流
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发表时间：
2015
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影响因子：
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通讯作者：
U. Hamenstaedt
中科院分区：
文献类型：
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作者：
U. Hamenstaedt
对于非例外定向曲面S，设Q（S）是面积为1的二次微分的模空间。证明了Q（S）存在一个Borel子集E，它在Teichmueller流F^t下不变，且对每个不变Borel概率测度都是满测度，并且F^t对E的限制在Weil-Petersson流中存在可测共轭.这种共轭性导致了F^t的不变Borel概率测度空间到Weil-Petersson流的不变Borel概率测度空间的连续注入H。映射H不是满射的，但它的像包含勒贝格刘维尔测度。
For a non-exceptional oriented surface S let Q(S) be the moduli space of area one quadratic differentials. We show that there is a Borel subset E of Q(S) which is invariant under the Teichmueller flow F^t and of full measure for every invariant Borel probability measure, and there is a measurable conjugacy of the restriction of F^t to E into the Weil-Petersson flow. This conjugacy induces a continuous injection H of the space of invariant Borel probability measures for F^t into the space of invariant Borel probability measures for the Weil-Petersson flow. The map H is not surjective, but its image contains the Lebesgue Liouville measure.