The Geometry of Regular Trees with the Faber-Krahn Property

Josef Leydold


In this paper we prove a Faber-Krahn-type inequality for regular trees and give a complete characterization of extremal trees. It extends a former result of the author. The main tools are rearrangements and perturbation of regular trees.

Mathematics Subject Classification: 58-99 (Global analysis, analysis on manifolds), 05C99 (Graph theory)

Keywords: regular tree, graph laplacian, Dirichlet eigenvalue problem, Faber-Krahn inequality, first eigenvalue, eigenfunction, rearrangment

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