非正曲流形中的周期积分
Period integrals in nonpositively curved manifolds
摘要：
我们提供了一个改进的半功率的日志到标准界的积分Laplace特征函数的余维2或更多的子流形，其中周围的空间是一个紧凑的黎曼流形与负截面曲率。对于其第二基本型与无限半径球面的第二基本型有很大不同的超曲面，我们提供了同样的改进。这一结果推广了Chen和Sogge、Sogge、Xi和Zhang以及作者以前在二维环境中得到的结果。
英文摘要：
We provide an improvement of a half power of log to standard bounds on integrals of Laplace eigenfunctions over submanifolds of codimension 2 or more, where the ambient space is a compact Riemannian manifold with negative sectional curvature. We provide the same improvement for hypersurfaces whose second fundamental form differs sufficiently from that of spheres of infinite radius. This result extends previous ones obtained in the 2-dimensional setting by Chen and Sogge; Sogge, Xi, and Zhang; and the author.
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