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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 Loewner's torus inequality ： ウィキペディア英語版 Loewner's torus inequality In differential geometry, Loewner's torus inequality is an inequality due to Charles Loewner. It relates the systole and the area of an arbitrary Riemannian metric on the 2-torus. ==Statement== In 1949 Charles Loewner proved that every metric on the 2-torus $\backslash mathbb\; T^2$ satisfies the optimal inequality :$\backslash operatorname^2\; \backslash leq\; \backslash frac(\backslash mathbb\; T^2),$ where "sys" is its systole, i.e. least length of a noncontractible loop. The constant appearing on the right hand side is the Hermite constant $\backslash gamma\_2$ in dimension 2, so that Loewner's torus inequality can be rewritten as :$\backslash operatorname^2\; \backslash leq\; \backslash gamma\_2\backslash ;\backslash operatorname(\backslash mathbb\; T^2).$ The inequality was first mentioned in the literature in . 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「Loewner's torus 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.