横向负弯曲叶理的拓扑结构和底谱

IF 0.7 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2025-09-29 DOI:10.1007/s10455-025-10020-5

Fabrice Baudoin

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引用次数: 0

摘要

我们证明了对于任何具有单连通负弯曲叶空间的黎曼叶化，叶的法向指数映射是一个微分同构。作为一个应用，如果叶是进一步极小子流形，我们给出了这种黎曼流形谱底的一个尖锐估计。我们对谱估计的证明也得到了水平拉普拉斯函数谱底的估计。

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Topology and bottom spectrum of transversally negatively curved foliations

We show that for any Riemannian foliation with a simply connected and negatively curved leaf space the normal exponential map of a leaf is a diffeomorphism. As an application, if the leaves are furthermore minimal submanifolds, we give a sharp estimate for the bottom of the spectrum of such a Riemannian manifold. Our proof of the spectral estimate also yields an estimate for the bottom of the spectrum of the horizontal Laplacian.

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.