Faber-Krahn Type Inequalities for Trees

Details Faber-Krahn Type Inequalities for Trees Faber-Krahn Type Inequalities for Trees

2003-12-15

arxiv.org/abs/math/0312287v1

Mathematics

Combinatorics

19 pages, 5 figures

Scientific paper

The Faber-Krahn theorem states that among all bounded domains with the same volume in ${\mathbb R}^n$ (with the standard Euclidean metric), a ball that has lowest first Dirichlet eigenvalue. Recently it has been shown that a similar result holds for (semi-)regular trees. In this article we show that such a theorem also hold for other classes of (not necessarily non-regular) trees. However, for these new results no couterparts in the world of the Laplace-Beltrami-operator on manifolds are known.

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