The geometry of regular trees with the Faber-Krahn property
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.
scientific article; zbMATH DE number 1741684