The Geometry of Regular Trees with the Faber-Krahn Property
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)
regular tree, graph laplacian, Dirichlet eigenvalue problem,
Faber-Krahn inequality, first eigenvalue, eigenfunction, rearrangment