Abstract
In this chapter, we collect some general facts about Riemannian manifolds and tubular neighbourhoods of a one-dimensional space. Moreover, we provide convergence results for small perturbations of a metric on a manifold. In the subsequent Chap. 6, we mostly consider so-called “graph-like manifolds” with exact product structure for an edge neighbourhood and with exact scaling behaviour of the vertex neighbourhoods, simplifying the reduction to the metric graph significantly.
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© 2011 Springer-Verlag Berlin Heidelberg
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Post, O. (2011). Manifolds, Tubular Neighbourhoods and Their Perturbations. In: Spectral Analysis on Graph-like Spaces. Lecture Notes in Mathematics(), vol 2039. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23840-6_5
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DOI: https://doi.org/10.1007/978-3-642-23840-6_5
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23839-0
Online ISBN: 978-3-642-23840-6
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