复双曲商的半经典测度

IF 2.5 1区 数学 Q1 MATHEMATICS
Jayadev Athreya, Semyon Dyatlov, Nicholas Miller
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引用次数: 0

摘要

研究紧复双曲商上拉普拉斯特征函数的半经典测度。这些商圈上的测地线流动是在不同方向上具有不同膨胀/收缩速率的双曲动力系统的一个模型。我们证明了任何半经典测度的支持要么等于整个球束,要么包含紧致浸没的完全测地线复子流形的球束。该证明采用了布尔格因-迪亚特洛夫(Bourgain-Dyatlov)的一维分形不确定性原理。数学。(2) 187(3): 825-867, 2018)沿着快速扩张/收缩方向,以类似于dyatlov - jsamzquel (Ann。Henri poincar, 2023)在量子猫映射的玩具模型中,以及依赖于拉特纳理论的快速不稳定/稳定轨迹闭包的描述。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Semiclassical Measures for Complex Hyperbolic Quotients

We study semiclassical measures for Laplacian eigenfunctions on compact complex hyperbolic quotients. Geodesic flows on these quotients are a model case of hyperbolic dynamical systems with different expansion/contraction rates in different directions. We show that the support of any semiclassical measure is either equal to the entire cosphere bundle or contains the cosphere bundle of a compact immersed totally geodesic complex submanifold.

The proof uses the one-dimensional fractal uncertainty principle of Bourgain–Dyatlov (Ann. Math. (2) 187(3):825–867, 2018) along the fast expanding/contracting directions, in a way similar to the work of Dyatlov–Jézéquel (Ann. Henri Poincaré, 2023) in the toy model of quantum cat maps, together with a description of the closures of fast unstable/stable trajectories relying on Ratner theory.

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来源期刊
CiteScore
3.70
自引率
4.50%
发文量
34
审稿时长
6-12 weeks
期刊介绍: Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.
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