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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 Bernstein's problem ： ウィキペディア英語版 Bernstein's problem In differential geometry, Bernstein's problem is as follows: if the graph of a function on R''n''−1 is a minimal surface in R''n'', does this imply that the function is linear? This is true in dimensions ''n'' at most 8, but false in dimensions ''n'' at least 9. The problem is named for Sergei Natanovich Bernstein who solved the case ''n'' = 3 in 1914. ==Statement== Suppose that ''f'' is a function of ''n'' − 1 real variables. The graph of ''f'' is a surface in R''n'', and the condition that this is a minimal surface is that ''f'' satisfies the minimal surface equation :$\backslash sum\_^\; \backslash frac\backslash frac\}(\backslash frac)^2\}\}\; =\; 0$ Bernstein's problem asks whether an ''entire'' function (a function defined throughout R''n''−1 ) that solves this equation is necessarily a degree-1 polynomial. 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「Bernstein's problem」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.