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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 Schoen–Yau conjecture ： ウィキペディア英語版 Schoen–Yau conjecture In mathematics, the Schoen–Yau conjecture is a disproved conjecture in hyperbolic geometry, named after the mathematicians Richard Schoen and Shing-Tung Yau. It was inspired by a theorem of Erhard Heinz (1952). One method of disproof is the use of Scherk surfaces, as used by Harold Rosenberg and Pascal Collin (2006). ==Setting and statement of the conjecture== Let $\backslash mathbb$ be the complex plane considered as a Riemannian manifold with its usual (flat) Riemannian metric. Let $\backslash mathbb$ denote the hyperbolic plane, i.e. the unit disc :$\backslash mathbb\; :=\; \backslash$ endowed with the hyperbolic metric :$\backslash mathrms^2\; =\; 4\; \backslash frac\; y^2\}.$ E. Heinz proved in 1952 that there can exist no harmonic diffeomorphism :$f\; :\; \backslash mathbb\; \backslash to\; \backslash mathbb.\; \backslash ,$ In light of this theorem, Schoen conjectured that there exists no harmonic diffeomorphism :$g\; :\; \backslash mathbb\; \backslash to\; \backslash mathbb.\; \backslash ,$ (It is not clear how Yau's name became associated with the conjecture: in unpublished correspondence with Harold Rosenberg, both Schoen and Yau identify Schoen as having postulated the conjecture). The Schoen(-Yau) conjecture has since been disproved. 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「Schoen–Yau 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.