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Manifolds, Tubular Neighbourhoods and Their Perturbations

  • Olaf PostEmail author
Chapter
  • 1.5k Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 2039)

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.

Keywords

Riemannian Manifold Quadratic Form Dirichlet Boundary Condition Neumann Boundary Condition Boundary Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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