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Stability Matters for Reaction–Diffusion–Equations on Metric Graphs Under the Anti-Kirchhoff Vertex Condition Read chapter Read first chapter

2020 | OriginalPaper | Chapter

Strong Isoperimetric Inequality for Tessellating Quantum Graphs

Author : Noema Nicolussi

Published in: Discrete and Continuous Models in the Theory of Networks

Publisher: Springer International Publishing

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Abstract

We investigate isoperimetric constants of infinite tessellating metric graphs. We introduce a curvature-like quantity, which plays the role of a metric graph analogue of discrete curvature notions for combinatorial tessellating graphs. Based on the definition in [26], we then prove a lower estimate and a criterium for positivity of the isoperimetric constant.

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previous chapter Signatures, Lifts, and Eigenvalues of Graphs
next chapter Spectral Monotonicity for Schrödinger Operators on Metric Graphs
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Metadata
Title
Strong Isoperimetric Inequality for Tessellating Quantum Graphs
Author
Noema Nicolussi
Copyright Year
2020
Book
Discrete and Continuous Models in the Theory of Networks

Print ISBN: 978-3-030-44096-1

Electronic ISBN: 978-3-030-44097-8

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-44097-8_14

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