关于覆盖空间和全空间的Steklov谱

IF 0.6 3区数学 Q3 MATHEMATICS Annals of Global Analysis and Geometry Pub Date : 2023-01-17 DOI:10.1007/s10455-023-09884-2

Panagiotis Polymerakis

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引用次数: 0

摘要

我们证明了具有边界和有界几何的黎曼流形上自然狄利克雷到诺依曼映射的存在性，使得狄利克雷谱的底部是正的。该映射被认为是边界的\（L^2）-空间中的一个稠密定义算子，它允许Friedrichs扩张。我们集中讨论了紧流形上黎曼主丛的覆盖空间和全空间上这个算子的谱。

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On the Steklov spectrum of covering spaces and total spaces

We show the existence of a natural Dirichlet-to-Neumann map on Riemannian manifolds with boundary and bounded geometry, such that the bottom of the Dirichlet spectrum is positive. This map regarded as a densely defined operator in the \(L^2\)-space of the boundary admits Friedrichs extension. We focus on the spectrum of this operator on covering spaces and total spaces of Riemannian principal bundles over compact manifolds.

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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.

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