The geometry of regular trees with the Faber-Krahn property
type: Item
instance of: scholarly article
title: The geometry of regular trees with the Faber-Krahn property
zbMATH Open document ID: 0999.05016
DOI: 10.1016/S0012-365X(01)00139-X
author: Josef Leydold
published in: Discrete Mathematics
publication date: 2002-05-15T00:00:00Z
review text: The author completes and extends his previous result on the Faber-Krahn type inequality for regular trees; see [Geom. Funct. Anal. 7, 364-378 (1997; Zbl 0892.05027)]. The ``classical'' Faber-Krahn theorem states that among all bounded domains \(D\subset \mathbb{R}^n\) with fixed volume a ball has lowest first Dirichlet eigenvalue. In this paper the author proves necessary and sufficient conditions of the Faber-Krahn property for \(d\)-regular trees and gives a complete characterization of external trees.
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 1741684
zbMATH Keywords: regular trees
zbMATH Keywords: Faber-Krahn theorem
zbMATH Keywords: Dirichlet eigenvalue
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1741684