Manifolds, Tubular Neighbourhoods and Their Perturbations
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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.
KeywordsRiemannian Manifold Quadratic Form Dirichlet Boundary Condition Neumann Boundary Condition Boundary Term
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