Harmonic measures for compact negatively curved manifolds
Harmonic measures for compact negatively curved manifolds
复制标题
紧凑负曲流形的谐波测量
DOI：
10.1007/bf02392709
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发表时间：
1997
期刊：
影响因子：
3.7
通讯作者：
U. Hamenstädt
中科院分区：
文献类型：
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作者：
U. Hamenstädt
令 M 为负截面曲率的 n 维紧致黎曼流形。测地线流 (pt 是 M 的单位切丛 T1M 上的光滑动力系统，由测地喷雾 X 生成。回想一下，T1M 允许四个自然叶状结构 W s~、W~、W s、W s~，它们在测地线流下是不变的。包含强稳定叶状结构 W~ 的 vETIM 的叶 W~(v) 由所有点 wETIM 组成，其属性为 Otw 之间的距离和 Otv 收敛到零作为 t--*c~ （其中我们可以使用 Sasaki 度量诱导的 TIM 上的距离） 稳定叶状结构 W ~ 到 v 的叶子 W~(v)=UteR~tw~(v ) ，强不稳定叶状结构 W ~ （或不稳定叶状结构 W ~）是 W ~ （或 W ~）在翻转下的图像。~：w--*-w 叶子。 W i (i=ss, su, s, u) 的 W~(v) 是 TIM 的平滑浸入子流形，连续依赖于 C~拓扑中的 v（参见 [Sh]），而且 W ~ 的切丛 T W i 是 TTIM 的 HSlder 连续子丛。零阶项在以下意义上从属于稳定叶状结构：
Let M be an n-dimensional compact Riemannian manifold of negative sectional curvature. The geodesic flow (pt is a smooth dynamical system on the unit tangent bundle T1M of M, generated by the geodesic spray X. Recall tha t T1M admits four natural foliations W s~, W ~, W s, W s~ which are invariant under the geodesic flow. The leaf W~(v) containing vETIM of the strong stable foliation W ~ consists of all points wETIM with the property tha t the distance between Otw and Otv converges to zero as t--*c~ (where we may use the distance on TIM induced by the Sasaki metric). The leaf W~(v) through v of the stable foliation W ~ is W~(v)=UteR~tw~(v ) , and the strong unstable foliation W ~ (or the unstable foliation W ~) is the image of W ~ (or W ~) under the flip .~: w--*-w. The leaf W~(v) of W i (i=ss, su, s, u) is a smoothly immersed submanifold of TIM depending continuously on v in the C~topo logy (see [Sh]). Moreover the tangent bundle T W i of W ~ is a HSlder-continuous subbundle of TTIM. The purpose of this paper is to investigate ergodic and analytic properties of secondorder differential operators L on TIM with HSlder-continuous coefficients and without zero-order terms which are subordinate to the stable foliation in the following sense: