Faber-Krahn Type Inequalities for Trees

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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.
19 pages, 5 figures

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Combinatorics, Spectral Theory, 05C35; 05C75; 05C05; 05C50

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http://salesiana.dossiersoluciones.com/handle/123456789/69604

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312287
 http://arxiv.org/abs/math/0312287

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arXiv