Spectral geometry of tubes
Résumé
The goal of this lecture is to give an account on spectral properties of tubular neighbourhoods of Riemannian manifolds. We focus on physical realisations when the base manifold is a curve in the three-dimensional Euclidean space, intensively studied during the last three decades because of physical motivations in quantum waveguides. These lecture notes consists of two parts:
1. General framework of arbitrary manifolds and dimensions: Light presentation and state of the art.
2. Special Euclidean tubes about curves: Detailed proofs and occasionally new results.
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