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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 Measurable Riemann mapping theorem ： ウィキペディア英語版 Measurable Riemann mapping theorem In mathematics, the measurable Riemann mapping theorem is a theorem proved in 1960 by Lars Ahlfors and Lipman Bers in complex analysis and geometric function theory. Contrary to its name, it is not a direct generalization of the Riemann mapping theorem, but instead a result concerning quasiconformal mappings and solutions of the Beltrami equation. The result was prefigured by earlier results of Charles Morrey from 1938 on quasi-linear elliptic partial differential equations. The theorem of Ahlfors and Bers states that if μ is a bounded measurable function on C with , then there is a unique solution ''f'' of the Beltrami equation :$\backslash partial\_\{\backslash overline\{z\}\}\; f(z)\; =\; \backslash mu(z)\; \backslash partial\_z\; f(z)$ for which ''f'' is a quasiconformal homeomorphism of C fixing the points 0, 1 and ∞. A similar result is true with C replaced by the unit disk D. Their proof used the Beurling transform, a singular integral operator. ==References== * * * * * * Category:Theorems in complex analysis8 |year=1996|pages=5–14}} 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「Measurable Riemann mapping theorem」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.