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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 Rn (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. (author's abstract) ; Series: Preprint Series / Department of Applied Statistics and Data Processing

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Türker Biyikoglu, Josef Leydold

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