On the Spectral Gap for Laplacians on Metric Graphs

P. Kurasov Dept. of Mathematics, Stockholm Univ., 106 91, Stockholm, Sweden

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We discuss lower and upper estimates for the spectral gap of the Laplace operator on a finite compact connected metric graph. It is shown that the best lower estimate is given by the spectral gap for the interval with the same total length as the original graph. An explicit upper estimate is given by generalizing Cheeger's approach developed originally for Riemannian manifolds.

DOI: 10.12693/APhysPolA.124.1060 PACS numbers: 03.65.Nk, 73.63.-b, 85.35.-p