Manifolds, Tubular Neighbourhoods and Their Perturbations

  • Olaf PostEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 2039)


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.


Riemannian Manifold Quadratic Form Dirichlet Boundary Condition Neumann Boundary Condition Boundary Term 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Mathematical Sciences Science LaboratoriesDurham UniversityDurhamUK

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