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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Rayleigh–Faber–Krahn inequality ： ウィキペディア英語版 Rayleigh–Faber–Krahn inequality In spectral geometry, the Rayleigh–Faber–Krahn inequality, named after its conjecturer, Lord Rayleigh, and two individuals who independently proved the conjecture, G. Faber and Edgar Krahn, is an inequality concerning the lowest Dirichlet eigenvalue of the Laplace operator on a bounded domain in $\backslash mathbb^n$, $n\; \backslash ge\; 2$. It states that the first Dirichlet eigenvalue is no less than the corresponding Dirichlet eigenvalue of a Euclidean ball having the same volume. Furthermore, the inequality is rigid in the sense that if the first Dirichlet eigenvalue is equal to that of the corresponding ball, then the domain must actually be a ball. More generally, the Faber–Krahn inequality holds in any Riemannian manifold in which the isoperimetric inequality holds. ==See also== * Hearing the shape of a drum 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Rayleigh–Faber–Krahn inequality」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.