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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 Willmore conjecture ： ウィキペディア英語版 Willmore conjecture In differential geometry, an area of mathematics, the Willmore conjecture is a lower bound on the Willmore energy of a torus. It is named after the English mathematician Tom Willmore, who conjectured it in 1965. A proof by Fernando Codá Marques and André Neves was announced in 2012 and published in 2013.〔〔 ==Willmore energy== (詳細はsmooth immersion of a compact, orientable surface. Giving ''M'' the Riemannian metric induced by ''v'', let ''H'' : ''M'' → R be the mean curvature (the arithmetic mean of the principal curvatures ''κ''1 and ''κ''2 at each point). In this notation, the ''Willmore energy'' ''W''(''M'') of ''M'' is given by :$W(M)\; =\; \backslash int\_M\; H^2\; \backslash ,\; dA.$ It is not hard to prove that the Willmore energy satisfies ''W''(''M'') ≥ 4''π'', with equality if and only if ''M'' is an embedded round sphere. 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「Willmore conjecture」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.