双曲n维流形端点的共形测度
Conformal measures associated to ends of hyperbolic n-manifolds
摘要：
设Gamma是作用在n维闭单位球上的非初等Kleinian群，并假设其Poincare级数收敛于指数α。设M_Gamma是开单位球的Gamma商。我们考虑某些族E = {E_1，...，E_p}，使得M_Gamma减去所有E_i的并是紧的。集合E_i称为M_Gamma的端点，E称为M_Gamma的端点的完全集合。我们表明，我们可以关联到E的每一端的尺寸α的共形措施，使两个措施对应于不同的结束是相互奇异的，如果非平凡的。在Gamma的极限集Lambda（Gamma）上的维度为alpha的Gamma的每个共形测度可以被写为与E中的端点相关联的这种共形测度的和。在3维情形下，我们的结果与Bishop和Jones的一些结果重叠.
英文摘要：
Let Gamma be a non-elementary Kleinian group acting on the closed n-dimensional unit ball and assume that its Poincare series converges at the exponent alpha. Let M_Gamma be the Gamma-quotient of the open unit ball. We consider certain families E = {E_1,...,E_p} of open subsets of M_Gamma such that M_Gamma minus the union of all E_i is compact. The sets E_i are called ends of M_Gamma and E is called a complete collection of ends for M_Gamma. We show that we can associate to each end in E a conformal measure of dimension alpha such that the two measures corresponding to different ends are mutually singular if non-trivial. Each conformal measure for Gamma of dimension alpha on the limit set Lambda(Gamma) of Gamma can be written as a sum of such conformal measures associated to ends in E. In dimension 3, our results overlap with some results of Bishop and Jones.
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